I don't believe there's a right answer to this. Surely the answer is always "it depends". And what it depends on is the interesting part of this whole debate.
We could have easily done http://TicketStumbler.com by bootstrapping, but YC moved our time line up by at least six months to a year, which we deemed very much worth the equity we gave up.
Now the decision is: does the money, leverage and ability to expand faster (in theory) we'd receive from plan A outweigh the amount of additional equity we'd have to give up.
'Is leverage and ability to expand faster, something you want?'
In other words. not can you play the Startup/VC game without a VC but, should you be playing that game at all? One of the points was that 10,000 users was a failure for a VC funded startup. That's not necessarily the case if you don't have an inherent valuation you need to aim for.
What's really hard for many founders (myself very much included) is telling your friends and family you're leaving this good job with health care benefits to do a startup. Having a name behind you makes this a lot easier; the YC money was almost irrelevant.
I can't think of any other benefit I'm missing. It seems to give a warm and fuzzy sense of security to a lot of people.
COBRA is a pretty bad deal though. Mine was almost $250. You can get a good Blue Cross plan for that much, or a simple disaster plan for much less.
What's a disaster plan? Google was not too helpful. It sounds like what I'd want.