You’d think that mirror technology would have advanced enough in the last century. But no, you still gotta crank your neck around just to frickin’ change lanes! There’s no reason why you can’t split the side mirrors and have them adjustable to different angles.
So what’s the deal?
It’s much easier/cheaper just to crank your head around.
It wouldn’t be easier if there were mirrors. As for cheaper, there’s all kinds of crap cars would be cheaper without.
Some sports car models have blind spots due to design. Before buying a car, it’s a good idea to test drive it and to research the model for things like blind spots.
As far as I can see the problem is simple latency. Car manufacturers have no incentive to modify the current mirrors, since car buyers do not have an immediate incentive to look for cars without blind spots. A car buyer (generally speaking) does not think: hey, lets buy this car because it’s safer for other traffic.
I may seem to generalize, but over here we’ve seen a discussion about truck safety: trucks have a blind spot that can easily taken away with a simple and cheap mirror (I think $ 10-20). Still they never did, even though there were several lethal accidents each year. Until last year the 27-year old daughter of a famous Dutch author died. Then legislation was passed that made such mirrors compulsory. This seems to prove the above general statement.
I do not believe truck drivers are bad people; just like everyone they just tend to ignore such remote risks.
The same reason most cars still have the damn space over the rear view mirror where the sun comes beaming in even with the visors down.
None of the 5 cars I’ve driven on a regular basis have had anything that I would consider a “blind spot,” but maybe my definition isn’t the same as yours.
Many people adjust the side mirrors in a way that shows them quite a bit of their own car’s body (and I used to do that, too). But it’s a waste of mirror space; you’re better off adjusting your side mirrors outward a little further, so you can’t see your own car in them at all. In my cars, setting the side mirrors this way has always given plenty of overlap between the rear-view and the side mirrors, and sufficient overlap between the side-view and my peripheral vision. I tend to check over my shoulder anyway, because it’s an old habit from learning to drive. But the mirrors don’t seem to lie.
And if that still doesn’t satisfy you, you can get a stick-on plastic chrome bubble mirror at an auto parts store for about $0.89 
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My mirrors won’t move far enough out to catch cars in the “traditional” blindspots – to the left or right, with their noses about even with the rear seat.
So buy a cheap stick-on convex mirror. Where’s the problem?
Kill two birds with one stone and buy a cheap internal convex mirror. I don’t like the round external ones because they take up a lot of space on the side mirror, but I used to have an internal one which was about the same size as the centre mirror, and it would clip on top of it - which helped block the sun. I could glance at it and see an entire rearward panorama all the way from the front passenger’s window to the driver’s one. It was possible to drive without turning my head at all. I still did, but that was due to the “don’t trust the mirrors” mantra that was drummed into me when I learned.
Some cars do have two element side mirrors as you describe.
this is from an Audi a4, for example. If you look closely you can see the vertical line dividing the two mirror segments:
Also, most blind spots result not so much from the design of the mirror, but how most people set them.
Here’s a link demonstrating a good technique:
How to adjust side mirrors