There is a fourth problem they solve: very early stage companies are willing to raise quick money on terrible terms as long as it doesn't actually set a valuation for their real seed round. Accelerators are positioned to do this because they can maintain a pretense that the shitty terms are made up for in mentoring and other services.

It would be much harder to raise a seed round on a 4M cap if you had just given an investor effectively a 1M cap 3 months before. But with accelerators that's not an issue!