Yes; all (most) skippers are simple taxi drivers and have no responsibility for you.
But...
I was on an individuals boat where a diver really didn't impress me with his kit. Looked stupid in so many ways. I, and everyone else, ignored that with the principle that it's their dive and their life. Not my problem. So I jumped in to almost perfect conditions and had a great 2 hour dive. Came up to discover the diver had drowned, body never discovered.
This incident has mildly bothered me in as far as I keep wondering if I should have taken more interest in that person and their perverse kit config. Was I selfish to not want to dive with them? I certainly didn't want to dive with them as it's not my responsibility to babysit anyone else. I'd like to think I would be more assertive nowadays should that every arise again... Until it happens, I won't know.
Now this is a long way from "Is a computer essential kit" and your point
@mac64 is completely valid; a computer isn't essential kit
[provided you've done your planning].
To not dive with a dive computer is nowadays a very rare thing. Certainly something a newbie wouldn't be doing.
If you and I were on the same boat and I'd noticed that you've no computer
and that I had taken an interest, I'd fully expect you to come out fighting with your reasoning which would put my mind at rest.
If I'd queried a newbie, or I didn't get a suitable response... ? Should I have a chat with the skipper? It's still not my problem, but the consequences of another drowning aren't great.