1. If they are offered an identical position at a company they believe in, they will leave. You won't be able to do anything to keep them around, so you have less ability to retain valuable employees. Hiring and training new employees is expensive.
2. They won't push back when bad decisions are made. Would you waste your time arguing about a bad decision if you didn't give a shit about the company? You want people who will work for the best interest of the company. Granted there comes a time when you need people to accept a decision, but you want their to be a discussion around those decisions.
3. They will negotiate for more salary than equity/options, giving them less incentive to help make the company succeed.
4. They are less likely to convince their friends to join the company. Stripe built an incredibly talented engineering team through mostly referrals[1]. You lose that if you are hiring people who won't convince their friends to join.
I'm sure I am missing many others, and all startups may not need a team so dedicated that they would give up their salary, but having a team who believes in your company does have real benefits.
[1]: http://firstround.com/review/How-Stripe-built-one-of-Silicon...