The RAW is clear. Unless I had a good reason to houserule, I would use it as written. I.e. allow it only when the floor or supporting walls are stone.
A good reason might be a campaign that almost never has enough stone for it. For example, one that took place primarily in a forest and had no suitable dungeons either. In an underwater campaign it would be reasonable to refluff it as a wall of coral, although it could also be usable as written.
However, even in such a case I'd be more likely to just guide the players towards other spells. Only if it was somehow important for a character concept would there be a reason to do otherwise.
Apparently not everyone agrees that the RAW is clear, so here's my rationale for it. This is the whole relevant paragraph, from beginning to end:
The wall can have any shape you desire, though it can't occupy the same space as a creature or object. The wall doesn't need to be vertical, or rest on any firm foundation. It must, however, merge with and be solidly supported by existing stone. Thus, you can use this spell to bridge a chasm or create a ramp.
So four statements here.
The first tells it can be shaped, but also limits it from occupying an object. The second gives more specifics: no need to be vertical, doesn't have to rest on the floor. The third again limits it to merging with stone for support. The last statement is just an example to illustrate what the earlier ones imply.
There is nothing there to imply that the third somehow only matters if you shape the wall specially. Instead, these are all rules about how you can use the spell, all must be followed. If you read it like that, there is no contradiction, so it's the natural way to read it.
Update: from wax_eagle's comment, a tweet from Mearls confirming that it must indeed be supported by stone.