You're throwing away the biggest advantage for the company allowing remote work -- hiring talent from anywhere. WFH has a lot of advantages for employees, but also for the employer. The main one being a diverse workforce.
What I've seen work, which I think still hits your goals of occasional face time, is to have a quarterly offsite for the whole company. Everyone works remotely, but once a quarter you find a nice location that is easy for everyone to get to, pay for their flights and hotels (and if you're really nice, their family too, or at least child care at home while they are gone), and then have a couple of days of quarterly planning, hacking sprints, and general social activities that don't involve alcohol or strenuous physical activity (but if people want to organize that for themselves they are welcome to do so).
Remember that for a US-based startup, the "hiring talent from anywhere" is easier said than done.
You've got to register your business in every state you have somebody working, get unemployment insurance and workers comp set up there, make sure you understand the local labor laws, etc., etc., etc. That's not even considering hiring outside the US.
It's a total pain in the butt and may not be worth it for a small company with limited person-power.
Oh I know. And I hate it. I run a remote company and have dealt with it.
I wish there was a company that existed to handle this for me. I just tell them I want to hire someone in state XXX and they set me up with whatever I need in that state. There are a bunch of companies that will get me 1/2 way (set up payroll but then tell me I'm on my own for insurance, for example).
But still, for the right person, it's worth the hassle. But this is also why some companies limit their remote work to certain states -- so they only have to do that stuff a few times.
I even think a quarterly off site is too much. Yearly is fine. Organizing flights, pet care, etc every 3 months is such a damn hassle, and I don't even have kids.
My friend did the math for a high-falutin position at a San Fran tech company requiring 3 days a week in office, and flying from New York to Cali every week was cost competitive.
What I've seen work, which I think still hits your goals of occasional face time, is to have a quarterly offsite for the whole company. Everyone works remotely, but once a quarter you find a nice location that is easy for everyone to get to, pay for their flights and hotels (and if you're really nice, their family too, or at least child care at home while they are gone), and then have a couple of days of quarterly planning, hacking sprints, and general social activities that don't involve alcohol or strenuous physical activity (but if people want to organize that for themselves they are welcome to do so).