What value does the expensive building offer the city if it's exactly the same?
You've actually just convinced me rent control might do a city good by pushing capital investors into more useful pursuits, rather than simply "investing in land" which effectively does nothing of value for people.
I do think it's silly to treat the symptom without fixing the main problem which is zoning law and permit restrictions on building more housing stock. But why not both?
Might as well add the Land Value Tax while we're at it