That might work for small groups. I've been at multiple dinners for 8+ people where, after we'd all "put in our share", the pot was still $50 (or more!) shy of the bill + tip. It's frustrating even as the non-host, since I know I carefully put in more than what my food + tip had cost.
Interesting, my experience is the opposite. Everyone rounds up a little bit and whoever is paying ends up with an excess. This is in Japan though, so the social dynamics are different from the US.
It's definitely the sort of thing that will vary a lot based on the group. I'm also at a place where I can afford to spend $50 or whatever to gauge the collective trustworthiness of a group of people.
Note that figuring out individual "shares" is more difficult in the US than many countries, what with tax and tip not being included in the menu prices.
