I agree with your analysis that it's increased competition for prime locations, but that seems to me purely descriptive. It's not a surprise, but it's still a problem :) And it's a problem that is masked by aggregate measures showing stable cost per square foot because those numbers are not "prime-locale" adjusted.
To be somewhat more precise, what we commonly describe as "buy a house" is actually much more than that. I can buy an amazing house-shaped structure in rural Wyoming for $200k. What I can't buy for that price is a stake in an environment where I want to base my career and family life for decades. The latter is what is crushing millennials.
Surely there are options besides the most prime locations, though. The problem we're describing isn't fundamentally an issue with price inflation, it's an issue with supply constraint. Price is how we decide who doesn't get a scarce good - more people want to live in those prime locations than we have supply for. You could cap prices at $1 and there would still be people who couldn't live there, simply due to lack of supply - we'd have to have some way of deciding who doesn't get to live there, and regardless of the mechanism, there will be people who desire to live there who are unable to.
We can either build more housing - which is a solution in some cases, but has constraints because of the realities of physics, and/or some people choose to live in a less prime location. That doesn't necessarily mean rural Wyoming - it maybe means a less accessible, attractive, or high-fashion suburb, or a midrange city.
IMO, it's helpful to view first houses as a stepping stone to another house - that $300k house in a nice part of town close to transit is a lot easier to get into when you have $100k of equity in your smaller house in a less nice part of town. My perception is that a lot of first-time buyers tend to have this idea that they must either buy in the perfect location or nowhere at all, then find that they can't meet the prices needed for that location, then just decide that owning is impossible. I don't know how true that is, but that's how this continuing discussion on my generation's home ownership seems to come across to me.
Historically it's been one of the most stable stores of wealth and predictably dependable forms of investment. You're going to live somewhere, so if you can capture your cost of housing as equity rather than paying it to someone else, you have an opportunity to build wealth reserves.
As you've alluded to, location is a factor. Specifically: the cost of land. Regardless of the price of building each square foot of housing, rising land values inflates the total cost of buying land to put that housing on. This is partially due to population growth. But it's almost entirely a self-inflicted problem. That problem is zoning.
If a slice of land can only be used to build a home for one family, and that slice of land is near things people want, it drives up the price of housing. If you were able to build a multiplex or condo tower on that land, the land would probably cost even more, but spread over more dense housing the price of land per square foot of housing would be much lower than for the single family home.
A second problem that's harder to address than waving a city planner's wand is infrastructure. Density requires transit (roads or otherwise), electricity, schools, sewers, water, etc. If municipalities don't plan for that it makes growing hard.
To be somewhat more precise, what we commonly describe as "buy a house" is actually much more than that. I can buy an amazing house-shaped structure in rural Wyoming for $200k. What I can't buy for that price is a stake in an environment where I want to base my career and family life for decades. The latter is what is crushing millennials.