If you know for a fact something is the right play, and you tell your team before...
But nobody listens, and they just go off in random directions like a bunch of stoned cats to do absolutely nothing of any import whatsoever, then get picked off one by one for the entire rest of the game and you lose even though you won your lane...
...should that be reportable? Refusing to communicate?
Having a difference in strategy is not reportable. There's no assigned leaders in League, and it's not against the rules to choose one's own idea over someone else's.
Beyond that, there's no such thing as "the right play"; there are plays that are objectively optimal in response to certain situations, sure, but that doesn't mean that all other potential tactics are bad and immediately invalidated.
It's only against the rules if someone deliberately chooses to do something with the intent to sabotage the match or otherwise harm their own team's chances of winning, and more often than not, bad plays are unintentional.
The entire game their ideas were obviously not working...
Well, first of all, if their ideas weren't working for the entire game, I'm doubtful even the optimal play could have turned things around even if it were pulled off. I have a feeling you're just being hyperbolic about it, but regardless.
Secondly; one can never know when things will turn up for them, and, unless they were doing the exact same things over and over again despite the enemy anticipating it every single time, I fail to see any reason why they should absolutely avoid trusting their judgement. Factors could change, the enemy could misplay or fail to anticipate whatever the other players had planned, etc.
...and they still refused to listen, even though I was being polite and matter-of-fact about it, not spamming pings or flaming anyone, just slowly progressing from suggestion to begging until our nexus exploded and there was nothing I could do to stop it.
And that is unfortunate, but sad as it is to say, people are not obligated to take others' advice, and sometimes people just won't listen. That's one of the sad truths of leadership; some people cannot be led. You could have every visible advantage and reason for people to defer to you, and they'd still trust their own judgement over yours.
And, as stated before, that's not against the rules unless it can be proven that it was with the explicit intent to sabotage the match.
Can I have 4 intermediate bots that respond to pings instead of human teammates? I feel like I'd climb much faster.
Don't ask for something you don't want. Intermediate bots are hardly good, and even if the somehow could respond to pings (which would probably be a friggin' disaster for Riot to try and code), they'd still only be capable of the most basic things; CS'ing, casting abilities, trading, and pushing.
Even bad players can ward; bots can't even do that much.
