(Yes, it's my first time applying to a startup)
That being said, I've only had one interview not result in a job offer of some sort (I've had some offers for contract work where I didn't get the full-time offer I consider successes) and I'm confident that had I been local and done an in-person interview I would have done much better (was my first remote/on the phone interview, and I imagine it must have been painful for the interviewer). When interviewing people, if they were good, I'm elated to see the follow-up. If they weren't, I dread it since it means I really need to start writing up rejection responses. What's the worst that'll happen, not getting the job?
I'm surprised more people don't do this. At the same time, do it once, and that's it. Understand that you likely won't get a response directly to the email, and the next contact you may have could be the yes or no.
If it didn't come up in the interview, make sure they understand what you like so much about their company, and what you can do for THEM. This isn't about you. Make it about them, and hopefully it will stick.
It always a surprise to me when throughout an interview, an interviewer talks about why the want the job by referring to how they'll benefit, rather than how the company will benefit from having them.