Interesting concept, although I don't know if I like it.
Here a couple of things to consider
Confusion can occur.
What happens if there are multiple floors pushed? Does it show the highest number? If it does, what happens to all the other floors? That could cause some confusion, especially those who see it for the first time; they could think that their floor is going to be skipped and will go to the highest one.
Users love progress.
Users really REALLY love progress. Why? Because it gives them a rough estimate of how much time is left. Whether it is a website, an app, or a physical object like a lift, users want to know how much time they are spending on something that's not so important.
Where on earth are we?
What if someone forgot to press their floor number and want to. Where are they? I don't know know! ACH! Now I have to wait more time! That's not good, from a usability standpoint of view. You want to make the process much easier for people. Also, what if there are more than 20 floors? That can easily happen in a hotel, office building, residential high rise, etc. Again, if they forgot to press their floor, or the press didn't go through and they noticed later on in the lift, it could cause huge problems as explained earlier.
In my opinion, I don't like the idea.