No it doesn't, that a big consumer app is considered 'mainstream' is an artifact of the fact that app got marketshare, its a dependent variable, not an independent variable.
Your claim is similar to ones that argue college is a waste of time, spend that four years doing things instead of learning stuff you'll never use. The fallacy of the college argument, and yours, is that structured learning has benefit in information gained over time at the start which is unmatched by unstructured learning.
Consider the time spent in an accelerator at those 'useless' mentoring meetings, they are with folks who have done a lot of different things, seen what is successful and what isn't, and more importantly know what traction 'feels' like when its happening. That lets one quickly learn the right stuff without having to waste time chasing ideas which aren't really having an impact.
I noticed that you backed off your argument a bit here: "I hear accelerator programs can slow you down in certain scenarios." If you're being honest with yourself then you can understand that "certain scenarios" is not "all scenarios" and by that reasoning your thesis fails. By that reasoning you would have to change your thesis "most likely" to maybe "possible".
If you want to reason about what makes a consumer app either a good fit or a bad fit for an accelerator that would be good to talk about. What sort of problems are ill suited to an accelerator environment and why? (and trust me, meeting frequency is not a good metric) There are a lot of accelerators out there [1], why not go through their funded projects and rank them consumer/non-consumer (you will need to define consumer app fairly precisely I suspect) and then bring some reasoning to the table that lets folks know how you arrived at the conclusion you did and why you believe it. We'd love to hear about it.