Not always. If you are running a cheap cassette sometimes it makes sense to just wear the chain and cassette out together. Replacing chains to preserve cassettes only makes sense if you are running expensive cassettes like Dura Ace, etc. It becomes simple math really.

Since August of last year I have purchased two mtb cassettes and one road cassette. And I've lost track of chains but i think i have used 3 mtb chains and i'm on my 2nd road chain. Everything was replaced based on the chain checker recommendations and cassette skipping. Excluding the road cassette, i replaced it because i got new wheels and i run cheap cassettes so i figured, what the hey.