There is no exact answer, but these are what I think are true!

1. Tatami mat
2. Shoes matter
3. Space problem

1. Tatami mat

Tatami mat is the traditional Japanese floor made of rice grass,
Which is soft and cozy to sleep on.
It use to be a major type of floor in Japan and the size of the room is measured by the number of tatami mats.
For example 6 tatami mats are the most common single bed room size in Japan.

2. Shoes matter

It might be also because of tatami mat, Japanese traditionally take off their shoes when they get into the house.
Tatami mat is soft and easy to be damaged, they do not wear shoes on tatami.
Therefore, the floor is treated as clean enough to put Futon and sleep on.

3. Space problem

Because it can be folded into two or three and put away to the storage, Futon was a space-saving way of using small space.
The room can be used as a study or dining room during a daytime, and a bed room during a night time.

These are what I(Japanese) think are the understandable reason for why Japanese use floor to sleep on.

If you are in Japan, try this traditional way and see how it fits you