It's not quite that simple. Building up can ruin the character of the neighborhood, which is often a big part of the allure.
I do think we're chronically underbuilding in a lot of places (SF being an extreme example), but the existence of steel and elevators is not a panacea for the "gentrification problem".
And this is inherently wrong, why? People (of whatever their net worth) vote, speak at meetings, and talk to their representatives to try and pursue outcomes that they prefer. One of those outcomes may be maintaining a particular character for a neighborhood. It's complicated. Greater good for the larger city or whatever and all that. But I don't see anything devious about residents having a say in what their community looks like.
It's sort of a Bavarian themed down-town and city in Washington state. Its allure and attraction to tourists depends on its theme.
I say I don't know if it's a great example because I have no direct evidence about prices, but I assume the reasonable volume of tourists and business must raise prices compared to other cities.