When home-values inflate, it's a wealth transfer from first-time buyers to retirees that are downsizing, selling a large home for a smaller one, putting the profits into stocks and bonds. To your point, that's not a net loss, just a wealth transfer. Note, it's not a net gain either. Building homes is a gain (usually), inflating asset prices are not.
As for the rising rent, that's part of inflation ... Anyway, you seem distressed that things are "really tough to represent in the statistics" but I assure you many of your concerns have been considered.
Doesn't technological progress complicate this question even further?
When I think of more expensive products, I think of computers, smartphones, etc. Yes, the new flagship products stay expensive, but that also represents new possibilities that weren't possible a decade ago (let alone a few decades ago).
But nowadays you can get a functioning computer that lets you browse the Internet, watch videos and do your emails for the price of a Raspberry Pi (and the investment of a separate keyboard, mouse, charger, SD card and TV - but those can be gotten for cheap as well).
Similarly, a lot of things that used to be expensive are now cheap.
So basically: technological progress is shifting the "quality" spectrum itself, in some cases very quickly, in some cases barely.
(I'm not saying you're wrong, I'm just curious how economists deal with questions like this)
Sometimes economists like to create some aggregate measure of increasing consumer choice by counting the number of SKUs available in a store. Big box stores pushing out Mom & Pop made that awkward. Now Amazon makes it tougher still.
Back in grad school, I was not aware of any consensus on the topic. I haven't kept up with it since.
One technique is to focus your research on products that are largely stable in quality. For example, wine glasses. Not plastic ones, but glass or crystal. They've got a fairly large distribution in "quality" or at least in price and yet had a fairly stable range of quality since the 1950s.
So their example was that if restaurant food hasn't increased in price by much, but basic groceries have then the 'inflation' seen by different groups may be very different.
Another example may be that if average housing costs increase just a bit, but the lowest rents have increased the most then cost of living changes could be significantly different between mid and low income families.
I'm not saying either of those examples accurately reflect how things are changing in the US (as I don't have the data to hand), but they are realistic scenarios.
My whole point is that adding things and then dividing by the sum of things is not a way to represent the reality that people face. You need to argue against that if you want to make a counter point. Just repeating what the person said that I responded to (after reading what he wrote) doesn't provide anything to the discussion.
The same applies to food. If you can afford eating in a restuarant for $20+ twice a day, you probably haven't seen any significant prise rises. But if you have trouble not spending more than $100 to feed four mouths a week, you probably a big decline in quality of your food since 2000. E.g. this requirement is hard to come by when you try to include fresh fruits.
Thus I'd say it's still an important point to consider.