Agree with just about everything you said and will add a few more observations.
I think not only do you need to be on a good team, but you need to be on a good team (preferably one that has one team per age group) that proactively advocates its players to coaches in advance of tournaments where the team will be playing. The attention span of coaches at recruiting events seems to be about 10 seconds, and unless a kid makes an all star game, or is playing in one of the small team events, the summer club season can be a real crap shoot.
My son played on a very mediocre team that happened to get into top quality tournaments such as Crab Feast, Legacy, and the Philly Invitational and to your point almost no coaches were watching them despite have a handful of legitimate DI prospects. What was most surprising is even when they were playing adjacent some strong teams such as 91 Extreme, Laxachusetts, Mesa Fresh, and others there were not a lot of coaches even watching those games. So my takeaway is you can't necessarily rely on the team circuit to get you much exposure.
I put a lot less credence on the mantra that if you are good they will find you, but as you pointed out prospect days are one way to get noticed even if you are not on a great team. That's what worked for my son, and now he has serious interest from several schools and it was all from individual stuff.
