In copyright disputes, evidence is everything. Evidence as to when something existed is probably the critical one.
Bingo, that's what I think, but I can't say how definitive that is or isn't here.
Copyright is in many ways like libel actions. You may be 100% able to initiate action, but can you afford to?
That's the other rub. If someone steals your stuff, it's likely to be no small amount of time, cost and effort to beat them back. Unless this is your livelihood, you'd have to seriously question if it's worth it.
Maybe you didn't read the whole thread. Registration being better wasn't my point. My point was, in the US, there is only one way to prove your ownership of copyrightable material.
Which would mean registration
would be better

but anyway......that isn't only way to prove ownership. Email is admissible evidence in court FYI. I'm not saying it would automatically overrule a copyright, but IMO it should. As mentioned earlier, "timing is everything" (or should be).
Not that any of this matters, it's all academic. None of us are ever going to have our songs ripped off nor have need to prove ownership.
And yet you copyright anyway

Yeah, as you pointed out, the odds are slim, but there's always that chance.
As has already been discussed and pointed out, no, it's not.
Whether or not loose or flakey attempts at proof may be acceptable doesn't really matter.
If you mean acceptable in court, obviously it does.