I have been following this discussion with great interest. I am one of those consultants that has actually seeked part of my compensation in form of equity, although not with early stage companies.
My specialty/niche is growth stage companies and I have selectively asked for equity with the right companies that I believe in, I know I can have impact in the successful growth of their company and I see a bright future.
I just recently got turned down by one of my client companies (about to go public in 2018) and was turned down. I was told that their agreement with VC backers did not allow equity distribution to non-employees.
However, because they could not pay me my full fee, I got creative with the exchange as I knew the COO personally. While some equity for my full fee would have been my preference, we made an agreement that he would personally introduce/endorse me to 3 CEOs in other companies. I probably could have asked for more. It was really an experiment.
For me personal introductions to CEOs is worth its weight in gold. So there are other forms of exchanges that are win/win. Just need to think outside the box.