do the founders really have a choice ? Most often raising money takes too long so you are left with "go with this or die" unless you are some rockstar startup.
Sure, the choice is in your second sentence there. Do the math, and if a round of funding is going to dilute you to the point that you aren't going to get any return from continuing to work on the company, cut your losses, let it die, and move on to the next thing. It might wound your pride, and nobody wants to see "their baby" die, but if continuing on means getting screwed, then don't do it.
Said a different way, consider the opportunity cost of continuing to work on this idea that will probably not be a big payout for you.
If your idea will improve the world in some useful way (and if the rest of the owners will let you continue on with the company), and if you think any replacement CEO won't be able to execute your idea to your satisfaction, it could be worth it for you to persist. Or it may be better to, as mindcrime said, cut your losses and work on your next idea that will improve the world.
Sure, the choice is in your second sentence there. Do the math, and if a round of funding is going to dilute you to the point that you aren't going to get any return from continuing to work on the company, cut your losses, let it die, and move on to the next thing. It might wound your pride, and nobody wants to see "their baby" die, but if continuing on means getting screwed, then don't do it.