Company's are not random. They are mainstream consumer apps. The next big consumer app = mainstream. Does that not make sense?
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.
I'm not saying all accelerators are good. Far from it. And I'm not saying accelerators don't have a ton of problems. I just don't think the article you wrote addresses any of them.
Or is your point that accelerator programs are aimed at companies in a particular stage and consumer apps don't need help through that stage. Surely the programs aren't that long and the next big thing could easily benefit from many of the benefits like networking and exposure?
If they just let you alone and let you build, what value would they be providing?
The value of an accelerator IS those mentors that harass you, ask you what you're building, and force you to challenge your assumptions.