Hiring is the most important thing your company is going to do, so limiting the pool for a little bit (or more) of "hassle" doesn't look wise, at best.
We're one of few early-stage startups we know of that sponsor H1B's at all so we're quite unique in this regard. We have 3 out of our team of 12. But we have to focus on recruiting team-members that have the highest probability of getting an H1 visa ultimately and having a US Masters degree in a STEM discipline greatly increases these chances. This is a conversation for a different thread but wanted to clarify as your assumption was mistaken.
