Under the "collect and prompt" scheme, you are still sampling randomly.
A random sample of users experiences perf issues, a random sample of users opts-in to the collection, you get a random-sample of data. (If you suggest they opt-in to continued collection, you might even get a continuous stream of samples from the same user.)
Yes, that data won't cover the people who don't have issues, but do you need to optimize for them? It also won't cover people who have issues but still don't opt-in, but do you think that is somehow correlated to the severity of the issue? Otherwise the data will be mostly unbiased. The variance will be higher than if you made it opt-out, but if you are doing sound statistics, you will have to handle that anyway.
The thing is, I think, that the users that opt-in to the collection aren't "a random sample", but rather "a sample of users biased towards certain profiles".
In part, AFAIA (but I've only limited statistical training) this is a well known feature of voluntary datasets. But IIRC they've also done user studies and compared those.
A random sample of users experiences perf issues, a random sample of users opts-in to the collection, you get a random-sample of data. (If you suggest they opt-in to continued collection, you might even get a continuous stream of samples from the same user.)
Yes, that data won't cover the people who don't have issues, but do you need to optimize for them? It also won't cover people who have issues but still don't opt-in, but do you think that is somehow correlated to the severity of the issue? Otherwise the data will be mostly unbiased. The variance will be higher than if you made it opt-out, but if you are doing sound statistics, you will have to handle that anyway.