Yeah. I think the issue is that the landlord is incentivized to extract maximum cash for the spot, which may be better for some other kind of venture (eg bank branch or whatever) which makes the restaurant's existence close to untenable in some locations. Public good or local quality or whatever does not factor in in any way.
There are probably better ways to do this than what I suggested.
Even if the landlords charged no rent, I would not expect to see profits increase significantly, rather I would expect prices to lower (and additional restaurants to open). Of course, if only a small(ish) number of restaurants get free rent, their profits would go up.
There are probably better ways to do this than what I suggested.