Sorry for the confusing response- Yes, you are correct on multiple points! First, currently the Mario game we have cannot be played independently. We are currently helping our participant play by doing the running when the key-map is set for them to "jump" or vise versa. My example was to highlight that we can re-map to any given key for a game, e.g. changing the brain-input to be mapped to "forward" instead of "jump".
Second, as you mentioned our kids cannot play any of these games independently. Typically the games have multiple input requirements with specific timing , which is much more difficult for the participant to handle, so we typically need to step in to help. That's one of the big inspirations of this game jam! Designing games with single inputs will let them play completely independently and help give them a greater sense of independence.
Regarding your game proposal- that sounds perfect! I think our participants would enjoy that quite a bit.