It is interesting to prevent men who have an obligation of tefila bitzibur from doing so in order to wait to accommodate women who don't
I'll go out on a limb and say that no women in your shul say kaddish?
I'm a gabbai at my shul. We've had minyanim up to 10 people until yesterday, and today we're limiting it to 20ish outdoors (Westchester and I believe rockland now have entered phase 2 as of today).
Do you know how difficult it is to decide who gets to come to minyan when you have EXACTLY a minyan? Obviously you want to make sure that the chiyuvim have an opportunity to say kaddish. Understand were a small community, and adding all of the factors - including the number of people who are immunocompromised and/or aren't ready to come back to minyan - even outdoors - leaves us with a small pool.
If I would get 17,18 people signed up, it would be easy to find a couple more and make a second minyan.
But if I would only get 12 or 13, who is the odd man out? Should I kick out the guy who is not a chiyuv, and has been to literally every minyan so that others can get a chance - I mean, he missed 2.5 months of minyan, so what is one more tefila? Should I kick out the teenager at the expense of the adults? Should I kick out the person from a neighboring town who is only here until his own shul re-opens?
At the end, B"H I am happy to report, that most times I was able to get two minyanim(three on shabbos morning ), and the few times I wasn't, I simply asked for volunteers. Some people were wonderful and willingly gave up their spots.
Back to the Issue of women and children for a moment - in my community Women do say kaddish, and do come to shul. (Before you go off on a tirade - save your breath. This is the psak of our Rov, and this is common across almost all of the shuls in Westchester). There are also many people (myself included) that have children that are old enough to come to minyan and daven. I would love to have my almost bar-mitzvah son come to daven with me and his older brothers. but neither of these should come at the expense of a minyan.
So what happens now when we fill up - I would imagine that if we get a full 20, I would probably start by excluding the kids, or better yet, recruiting more people and splitting one minyan into two.
One more note: While we could easily return to regular scheduled minyan and not need people to signup, we are still requiring signups to help make sure we a) get enough people b) Don't have too many and c) for Contact tracing