"More ubers actually mean less vehicles since people who would otherwise drive and park all day would take an uber"
That's a pretty strong claim - where I've see uber operate the vast majority of fares seem to be people who were taking taxis anyway, they just prefer uber. Do you have evidence that uber is actually eating into private car usage in any significant way in a dense metro area?
You would argue that more and more ubers would come. But uber drivers would see they wouldn't be making enough money so they wouldn't do that.