Most cars have a minimum speed you must be driving in order to engage cruise control. What is the rationale? Why not allow it to be set at any given speed?
If I had to guess
A)The ride would be too jerky at a lower speed. It’s rare that you’re ‘cruising’ at a specific speed when you’re driving that slow anyways.
B)You really should be paying attention and have you’re foot ready if you’re driving in a parking lot or alley. Being able to use CC in those locations would probably just be asking for problems.
I notice that it varies from car to car, even within a make.
But, I believe it has something to do with automatic transmissions shifting too often on slightly uneven terrain.
My car has a standard transmission, but still has a minimum set speed for cruise.
My understanding is that when you are going slowly, you are doing that for a reason. That is, it is likely the situation will change more quickly than you could react if you were going faster. In those situations, cruise control is the opposite of what you want; you need to be in complete control of the vehicle to be able to react to the changing situations.
I’ve found they generally engage at around 35 mph. The rationale for cruise is to avoid/relieve fatigue that results from holding a more or less steady speed for long periods, such as highway trips. On that basis, there’s no need for it to engage at a lower speed, and even 35 mph is a generously low speed for it. As Joey P (and on edit, excavating) suggests, at those lower speeds cruise could cause problems while not providing any real benefit.
My 97 Lexus es300 has a min cruise speed of 25 mph.
My Toyota Rav4 Sport will let you set the cruise control at exactly 25 mph but no lower. I have tested it just out of idle curiosity but the point is the same. I can’t imagine a scenario where using the cruise control below that speed would be of any benefit to anyone and could be dangerous.
I am not a fan of cruise control in general because I believe it invites complacency and lack of positive control of the vehicle. If I lived in West Texas, I might feel differently but I drive on plenty of rural roads in New England as it is and have never felt that it added any benefit so I don’t use mine. Your feet have to rest somewhere anyway so they might as well be on the accelerator and positioned to hit the brakes at any instant as opposed to resting limp somewhere else on the floor. It shouldn’t take any conscious effort to keep your feet where they need to be and maintain a steady speed so I don’t see any real benefit to cruise control at all especially when combined with the minor safety concerns. Cruise control is never going to help you avoid an accident and it could potentially hurt so why use it at all?
I often wanted cruise control to work at a fairly low speed when I was going through a school zone. It could keep me from inadvertently matching someone else’s car and speeding by mistake.
Not having a reason to need it isn’t really a good justification for the feature - it would be easier to not put the restriction in…and if no one really uses it, then it just wouldn’t be used. The fact that the restriction is there means there indicates that there is a positive reason for it.
If safety is the concern, shouldn’t cruise control stop working above a certain speed, too? Can I set the cruise control for 100MPH?
My Mazdaspeed 3 goes down to at least 30 mph; any lower than that, and I tend to be losing my shit at the idiot in front of me or in legitimately heavy traffic, so I can’t imagine needing it. That said, I’m familiar w/ plenty of long city streets w/ relatively few stops with a stated speed limit of 25 mph; that’s where I tend to stick it at 30.
Useful in speed zones
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CC trades control over vehicle speed for knowledge of constant vehicle speed without having to take your eyes off the road. So I question your contention that CC is a minor safety concern, and opine that it may be safer to not have to glance at your speedometer frequently to determine your speed or not glance at it at all and drive too fast or slow.
fWIW I have never seen a car that had a maximum set speed for the cruise.
I know for a fact that the cruise will set and hold 135 on a turbo Volvo. 
I agree with you to a large extent – I only use it in certain circumstances. I had enough cars without cruise control in my younger days to be used to just using my right foot, and also believe that in traffic, one makes a LOT of nearly subconscious speed adjustments that help to maintain safe gaps, get out of blind spots quickly, etc., and all that is lost with cruise control
If you are driving and you see something weird going on ahead, you will normally start to lift off the throttle and cover the brake without even really thinking about it…with the cruise set, some people might not do this (or at least not do it nearly as quickly) and thus be less prepared for a possible bad situation.
For those reasons, I don’t really ever use it when there is moderate or heavy traffic…I don’t want to adjust it or cancel/re-set it all the time, as that defeats the purpose.
However, in very light traffic, it is nice to be able to maintain an exact speed without having to constantly monitor it. Sometimes people who don’t use it will speed up to pass and then slowly lose speed when in front, causing me to have to re-pass them…this can repeat over and over on a long stretch and be pretty annoying. It also keeps your speed in check – if you only want to go x mph over the speed limit, you can do so without accidentally speeding up on a downhill run and getting a ticket.
Same for my '98 Corolla.
Some European cars have a CC setting which fixes the maximum speed. If you are in a 30mph zone, you can set it to 30 and it will not go any faster. It can be useful although on a down slope you can still pick up speed.
CC on trucks will also set a speed and apply the brakes if it is exceeded. The latest systems are even more sophisticated, and will slow down if you get too close to the vehicle in front. Volvo Trucks - Adaptive Cruise Control keeps safe distance - YouTube
Of course if you really mess up - you can still rely on the systems to get you out of the poo: Volvo Trucks - Emergency braking at its best! - YouTube
I found out that my BMW will shut the cruise control down when you reach a critical low-fuel level.
Almost like the car was saying, “Hey, Dummy! I’m not just gonna keep going till I run out of gas!”
Almost the same for my '08 Corolla. The main street in Norwich VT is 25 and strictly enforced so I would like to use by CC at 25. But it seems to only engage at a hair over 25. So I risk it! 
Although the rationale about using cruise control at low speeds being unsafe is (IMO) generally true, cruise controls evolved this way due to mechanical limitations.
Before true cruise control my dad told me that way back (pre & early 50s) some cars had a manual, cable ‘throttle’ on the dash (similar to manual chokes). Worked just like the gas pedal except it didn’t spring back. It may have had some kind of safety release (i would hope) but I don’t know.
Before computers came to cars cruise control units consisted of a vacuum/servo mechanism linked mechanically to the speedometer. Consequently they weren’t terribly precise. In the 80s vacuum servos & cables got replaced with (analog) electronic sensors & motors. These were better but still far from perfect. Also remember the math: The difference between 10mph and 15mph is only 5mph but its also 50%, whereas 60 to 65 is less than 5%. This combined with the safety issue meant that car makers had good reason to set the minimum cruise control speed at 30mph or so.
With today’s sophisticated computer control I’ll bet you could make a unit that could be set to any speed no matter how slow. Absolutely with an electric/hybrid. But even with a gas engine, given how smoothly they run (again because of computers) I’d also bet it would work pretty well even at really slow speeds.
I had the occasion to see it used at about 23 MPH in a Nissan Versa today.
I seem to remember reading of a car in which you set the mph you wanted by number. You could set it at 0 and slowly dial up to cruising, and back. No idea now what it might have been. My '41 Ford had a hand throttle. Handy for working on the engine, climbing a long hill, etc. No safety release, so you couldn’t shift on the long hill, without pushing it in first.