Handyman here. I do quite a bit of microwave/vent hood conversions. IMO it’s a good swap. Micros are cheap. However, on thing to consider is whether or not the backsplash material goes high enough up to cover for the shorter height vent hood.
I can certainly understand not wanting to have an over the range microwave, but you are vastly overestimating the negatives. I’ve had one for the last 15 years, and have never considered moving to a counter-top model.
I have never even been remotely close to being burned by reaching over the stove. When you are cooking you are always putting your hands and arms much closer to the burner and food than when you use the microwave. I could put all of my burners on full gas, with no pans on top, and still use the microwave with no burning of flesh. This is really a non-issue.
Also, they are made to be over the range. These are not simply counter-top models that are placed above the range; they are built for it (and their cost shows it; they are more expensive than counter-top models). All that I have seen have a built in fan and vent to get rid of steam and smoke.
As far as reaching up, I think for someone very short or very old, this could certainly be a consideration. I am 5’9" and have never thought this is “reaching up”. As someone else said, it is basically at chin level for me. My wife is 5’3" and uses it all the time. Maybe she harbors a deep inner resentment at the height of the microwave, but if so she has never expressed it to me. My daughter is about 5’1" and has used the microwave regularly for a couple of years with no issue.
Also, you seem to indicate that “more counter space” is a ridiculous benefit. Isn’t lack of counter space one of the biggest complaints people have about their kitchen? At least people who actually use it to cook. We have a very decently sized kitchen, but there are many times I wouldn’t mind a little more space, and I am in no hurry to block off 4-6 square feet for a microwave that works perfectly well where it is.
As always, YMMV, but I would be very hard pressed to consider this the “worst kitchen idea ever”
Yeah my initial reaction was that it would be a hazard. However for those like me in the UK it seems that an over hob microwave would be at the height of aneye level grill. We don’t have any trouble reaching over or up to those, although admittedly toast is not normally liquid. Therefore I think this is unheard of in the UK because it would interfere with said eye level grills and because even if we don’t have one it looks weird, icky and must be dangerous 
Well I am taller than the woman in the OP, and I have had an over-the-range microwave and I did not like it. And let me say that no, standing on a stepstool is not going to help all that much.
I found it hard to see the controls, awkward to get things out (although I have to say, it never seemed unsafe–the stuff wasn’t that hot), and awkward to clean it. Other people in my household were at least 5’10" and growing and they had no problem. Only I had the problem, and while it was no more of an annoyance than not being able to see what was on the top shelf of the closet, when the option arose to have it on the counter instead, I did that and it made things much easier.
The new thing in microwaves seems to be putting them in a drawer. I’m not really down with that idea either, but I think I like it better than the over-the-range option.
I’ve never experienced a problem with the position of my microwave and I’m the same height as the OP’s mom. Of course, I can see there might be some issues for an elderly person if she is not steady on her feet.
My microwave sits up on a shelf to the right of the stove, similar to this, but I assume it would be the same height as an over-the-stove microwave. I’m about 5’4" and have no trouble using it.
Our microwave is over the stove, my 5’3" wife has no problems with it at all.
My wife is 5’5" and has a herniated disc that makes it difficult for her to tilt her head beyond the normal horizontal orientation. She has no problems at all using our over-the-range microwave. We’ve had it for ~8 years and steam from boiling things has never caused it to do anything unusual. It’s designed to go where it is (built-in extractor fan, etc.)
The only problem I can see for Mom is that she may not be able to see the bottom surface to know when it needs cleaning (or when it’s clean after she’s wiped it).
Really! Imagine that, something installed above the countertop really doesn’t use up countertop space! But seriously, ours has a built-in fan that acts as an exhaust. Our range isn’t huge so you’re not leaning over pots and pans on the stove to access the microwave. And there’s no underneath to accumulate crumbs and roly-poly bits of food, or liquid spills. I think it’s very nice.
I like that set up. Of course, you still need a hood, but that is a much more sensible and convenient arrangement.
Consider buying some microwave-safe beakers or pitchers (with handles!) for her. Get only larger sizes, so that the liquid only fills them about halfway – that will reduce sloshing, and the handles make dropping one less likely.
Encourage her to always use a large size, so that it’s only half full of liquid. And to always use these containers, rather than just putting a dish or plate directly in the microwave. (If necessary, convince her that these ‘special containers’ work better in the microwave than regular cups or bowls, and that always having the container only half-full makes the liquid heat up faster (saving electricity). Telling little white lies to keep an 85-year-old parent safer is OK!
No probs, Ace - your mom’s travails can be solved in style.