That's an example of a reply that is "unsolicited" and "also irrelevant", by your criteria.
I'm not trying to defend that combo here. You said such a screed is "also irrelevant", right?
That means even if a reply wasn't irrelevant, even if it was a useful response, it would still be unsolicited. Right?
Is that what you intended to say? Am I misreading something?
If you send someone an invite to a discussion, they're invited, whether you meant to or not. At least long enough to send a single reply (which may be multiple tweets).
Whether their response is a polite "you tagged the wrong person" or some awful screed does not change whether a solicitation happened. Especially because tagging someone is not a request for any specific sort of reply.
Relatedly, if someone is eavesdropping in public and steps into a conversation to make the most wonderful helpful and loved comment in the world, doing that was still unsolicited.
Also tagging does not necessarily request a reply at all.
This is silly and will go in circles so I will finish by just saying.. What the fuck did you just fucking say about me, you little bitch? ....
And that's what twitter is, brief conversations.