Yes, strictly true, but friendship is worth it, no? Do you spend a couple of hours with a friend and then hand each other bills for the hours? Clearly there was a[n opportunity] cost to both of you, after all. Just spending time together without charging would be like randomly handing over a wad of cash ...

>Buy for $x, have and not sell for $x, same mathematically.

They're not the same.

£20 item to buy, I have £100; buying leaves me £80. Either, I have £100; not buying/selling leaves me £100 £20 item I own, I have £100; selling leaves me £120.

In the first case maybe I can't make rent now. In the last case I have more cash, but then I need to spend money if I want entertainment/utility that the item had. In the first case I lose 25% of my cash; in the last I gain 20% (this matters when you're sharing your money across different needs).

If you're trying to make rent right now it makes a difference. In the long run it's looking at X income and comparing how much better/worse off you'd be with X-1 and X+1 income, and those two deltas are almost the same. The fluctuation in value of the object will make a bigger difference than the technicalities of buying versus selling.