In general, the mobile phone industry has done a pretty good job encouraging their userbase to forget that their batteries are replaceable, so I don't think that most users would consider that as a remediation step off the top of their head.
I think it's plain that the best solution would be informing the user of the problem and letting them choose between behaviors (or, you know, replace the battery), but between slow usage and random shutdowns, I would personally choose the former.
I wonder if there have been any studies on how many users, once the toggle had been added, switched it from the (default) throttling behavior to the shutdown behavior? I'd be curious to see if I'm in the minority there.