I think you must live in my town! That's exactly the format we have.
The pros are that it's participatory and anyone can speak up on an issue. There is a Board of Selectmen that meets and, of course, people can (and should) speak on particular issues at those meetings, to influence what items get on the Town Meeting agenda (called a Warrant). Still, there is open discussion at the TM. Selectmen's meetings (and most major committee meetings) are televised on the local cable channel so people can watch them if they want and if they are unable to get out.
The cons are that only a small percentage of people actually attend any of the meetings, so decisions are made by a group of regulars. And yes, any whack job can get up and ramble/rant about something. The school budget is a huge chunk of the overall, so there is a bit of a dividing line between long time, retired residents (who either are on fixed incomes or who don't understand or care about the huge increase in, say, special needs curricula/staff) and the parents of the students who want more services and who, in general, are better informed or at lest more invested in the schools. And the senior citizens who are less mobile are unable to get to meetings if they don't drive or if they don't go out at night.
But any issue can be polarizing within the school, so there are often 2 sides among the parents. As you say, having both parents able to vote means hiring a babysitter until 11 PM on Night #1 (tough enough, plus an expense) and then having a sitter on standby in case the meeting resumes the next night. Our TMs usually occur on a Saturday, which one would think offers more flexibility, but even so, it's a 5-6 hour commitment with adjournment and continuation on Monday night. Then there are occasional "special town meetings" to deal with 1-2 specific issues. So what we find is that parents will flood the meeting when there is a school issue on the agenda, and then leave en masse when that vote is done.
We also find that there is very little turn-out for town elections (which are inexplicably held on a day other than Election Day), and most people run unopposed for offices. If we have 2 Selectman seats open, at most we have 3 people running. Most of them are incumbents or people who served in the past - very few new faces. So I think that people are pretty divided among those who participate and the vast majority who do not, either in serving in office or in attending meetings.