Not at all - in fact SugarCube does saves very well. Axma does about the same thing, giving the user about six save slots that remember game state.
I just appreciate that I don’t have to think about the user interface and layout much in AXMA. You can choose layouts with a side picture or a background in several formats, and basic usability is covered for text size and audio and screen animation. The UI also reconfigures the screen real-estate automatically on the fly. On mobile or when the browser is too small, the side picture and menu are moved to the bottom of the screen.
Here’s the basic interface with the “gear” options opened:
Here’s what happens when the screen size is reduced: (notice the menu which says “introduction” moves to the bottom, along with a picture thumbnail the player can click on to see it)