As far as I know, the "no save state" thing is something the game has originally, and it causes some problems (one of them related to a password that won't accept for some reason when you use save-states. others being text glitches, for example).
Also as far as I know, it's present in the sequel because of the "real time clock" feature can create problems using save-states. In both cases is logical, as these games weren't intended to be played with emulators, lol.
I don't like save states that much either, they usually remove a lot of the challenge of most games, I would go as far to say that they can ruin the experience of a game if you're playing it for the first time, although of course it's only my opinion, and they are very welcome for games that can't save or don't have passwords, and you need to quit fast, or for testing purposses, for example.
Super Shell Monsters Story thankfully has "save spots" for dungeons or caves and the posibility of warping outside of most places so you can save on the overworld.