If there's an afterlife and I ever have a chance to ask God how you should measure housing costs in the consumer price index, I'll be intrigued at the answer, because no human has figured it out.
You can weight the value of new houses relatively heavily or you can go to more of a rental-equivalence measure, because it's not obvious. Housing isn't something that you use up all at once like a cup of coffee; but on the other hand, if you only look at it over the life of the housing stock, then you're going to miss some of that upfront cost. Every country has its own way of trying to deal with this.
What we can say, though, about the inflation numbers that we're seeing right now is this. The fact that housing has gone up so much means there will be continued upward pressure, and measured inflation for a long time as a result of it. That's one reason that we worry about inflation expectations becoming unanchored, because some of these things have a long tail; and the longer inflation stays above 2%, the likelier it is that people will say that they just don't believe the 2% target anymore.