The classic Roombas from a decade or so ago worked without any sort of mapping or camera at all -- they basically did a version of the "run and tumble" algorithm used by many bacteria -- go in one direction until you can't any more then go off in a random new one. It may not be efficient but it does work for covering territory.
I think the only reason for mapping is to be able to block off 'no go' areas (no escaping out the front door!) and to be able to go home to the charger.
For the actual cleaning, random works great.
Sounds like it would only work for a single room with not too many obstacles.
I guess the mapping capabilities vary greatly between vendors. I had a first gen Mi Robot vacuum and it was amazing. It would map the entire floor with all the rooms, then go room by room in a zigzag pattern, then repeat each room, having no issues going from one room to another and avoiding obstacles. It also made sure not to fall down the stairs. Then later it broke and I bought a more noname model and despite having lidar tower, it didn't perform as well as Xiaomi vacuum did. It worked for a single room, but anything more and it would get lost.