Actually, VDP RAM isn't memory mapped on any platform that I know of. But other systems have CPU-addressable memory that you could store a shadow copy of data in at least. The paltry 256 bytes on the TI-99/4A, though, are far from enough in many cases.
On the contrary, many 8-bits had memory mapped video. Commodore (VIC/64/Amiga), Sinclair (Spectrum, zx81, zx80, dist by Timex in the US) Atari, VT100 ... etc etc. Not that there weren't machines with distinct video RAM, the Commodore PET had specific video memory, though it was still mapped into the address space like a modern PC video card. Having the video RAM in a inaccessible (I/O bus) location was rare.
The reason was simple, at that point in time only a relatively small amount of RAM was needed for the machines and it ended up being faster than the CPU. So much so that you could assign 50% of the RAM bandwidth to the video subsystem without impacting the speed of the processor at all.
The ZX81, however, was a bit of a foreshadowing of things to come. It was built really, really, cheaply and they used really cheap DRAM. This cheap RAM wasn't fast enough to feed both the CPU and the video at the same time so the CPU was basically turned off when the video was being displayed (In fact it was physically used as a counter chip by the ultra cheap video controller).
Nowadays people want astronomical quantities of RAM so it basically has to be the cheapest design possible; this type of RAM can't keep up with just one CPU, let alone multiple CPUs and a video controller. So the video controller has to reduce the performance of the main CPUs by stealing cycles, or it gets it's own RAM.
Note: There are several Intel video controllers for PC clones that use main memory as the video RAM, they get added as a cheap motherboard video controller. Because of the fact that they're using slow RAM and stealing cycles from the CPU these are rightfully seen as very low performance.
On the other side, a common mistake for designs with distinct video RAM is that the CPU only ever needs to write to this RAM, unfortunately the problem is frequently only recognised in production.