The emulator needs to pop up 2 terminal windows so that we can log in to the BBS. We do that, and a colorful menu is displayed on each of them. At this point, we save a snapshot and shut down the host computer. Later, we start the host computer, then start the emulator, and then try to resume the snapshot. Each terminal window remains blank, which is not the correct state. The guest OS (a DOS BBS) is in the state where it is showing a colorful menu, but we can't see it at all. Our terminals, being separate from the emulator and without an ability to save/restore snapshots, are inconsistent with the emulated guest OS.
In the above example, the guest OS (a DOS BBS) never did any kernel syscalls related to PTY operating mode. It directly acted on serial port hardware. There is no PTY, and adding one (where?) doesn't help.
Fundamentally, the emulator needs to be able to save/restore all terminal state. That even includes stuff like incomplete escape sequences, such as when just the first byte of the escape sequence has been passed to the terminal.