If the game designers had coding using the BIOS, this would not be a problem.
Now, poking directly into memory is not strictly using the BIOS, but it works because of the circuitry and can generally be expected to work on any CGA clone. But doing stupid things like plinking the 6845 directly for a simple mode change when the BIOS call is just as fast breaks some software. There were patches for lots of broken software that did that.
Onto the broader philosophy question. The PCjr is what it is. The Tandy guys did it right by moving the video memory window to the *TOP* of memory, where the assumption is that the top is more like 640K, not 128K. That way you get contiguous memory for DOS without the hassle of a device driver.
If you want a machine like that though, why not just get a Tandy or a PC? Without the charming cartridge slots and wireless keyboard of course. By the time you hack a Jr to replace the video subsystem, it's not really a Jr anymore, is it? That was part of my distaste for the VGA sidecar. A Jr with the onboard video neutered and replaced with VGA is just another clone at that point.
The DMA controller is a whole other problem. Adding the DMA controller only helps the floppy drive, nothing else. If won't let you add sound card, hard disk adapter, or any other peripheral that requires DMA. The bus only accommodates one DMA channel, and it's reserved for use with the floppy. And it's wired that way too.
So even when doing serial communications, typing or screen scrolling can cause you to lose characters on the 8250 UART, regardless of DMA or not.
Putting the keyboard on the NMI interrupt instead of IRQ 1 was just dumb ... Polling for the floppy drive is forgivable, as most OSes couldn't make good use of DMA back then anyway. But the keyboard interface to the CPU using NMI was just one shortcut too many.