actually, i remember there WERE at least two native DOS programs that run as TSR and would save/load state on certain key combination Some games would recover on its own when faced with glitches (e.g screwy palette or the panning was off). Of course, some games didnt work.
Unfortunately i cant recall what either one was called. (maybe it'll come to me later). The point is, it's been done before and there's no reason why dosbox cant dump states. Playstation, Sega, N64 and even PS2 emulators do it.
Having DOSBOX cover all permutations of PC hardware is most likely next to impossible, but at least developers can try dump the basics like memory, ?GA and beeper state. Label it a "experimental" feature. If it works, good, if it doesnt, tough luck 😀
PS. Here's a very real example of why s. states are necessary. I'm playing Metal Mutant right now. It plays digitized audio only through PC speaker. Needless to say it's quite distorted, and not due to my slow hardware. There's a puzzle in the game where you need to listen to sequence of tones and then replay the correct sequence using buttons. I'm STUCK.