The system right now is nice. Problem is that there's a lack of dungeons to do. There's V15, Glow, Ares and Warehouse. There's a small sewer system below reno too. That's not much really.
Keeping these are public is fine, there shouldn't be a major problem if there's a good amount of them. Right now you can safely do V15 and Glow and you'll rarely run into other players.
Dungeons being possible to solo is fine in my book too. The best situation would be a large amount of dungeons, where some are soloable (eg: right now glow and v15) and some dungeons would force you to use a team (eg: Ares). This way there's something for everyone.
I'm 95% agains't TLA dungeons. Yes they are all nice and dandy, but they completely kill any player interaction, bullets or not. You've got all these players doing these private dungeons, never leaving their bases. Causing towns and other places to always be dead. It's vital to avoid that in Reloaded, make sure players interact with eachother one way or another.
A good thing from TLA could be those random raiders camps that spawn on the worldmap. Public yes, but not as easily scouted since their location is random. NPC's invading towns is also a neat little thing i'd love to see. having raiders invade NCR for example, tie some rewards to helping a town out. (points for each damage you inflict on hostile NPC's that invade, exchangable for drugs/caps/ammo.) Hell you could make NCR a joinable faction, and slap some repeatable missions on it where random pve players can work together.
MMO's are social things, so anything that forces player interaction is a good thing. And I agree that some players who absolutely hate pvp should not be forced into it, and should have their own set of features to play with. Caravans are already nice, but should have rep penalties bound to shooting friendlies to help prevent teambleeding/griefing.