Bragi,
I just finished collecting all the TP’s about a week ago, and there were a couple reasons I did it. First, I started in Fort Troy, which is not a very exciting place to stay. I wanted to get to Hadesheim to see the shops and “the capital,” where there are “TT style” tailors, clothiers, etc. Fort Troy was so far from Hadesheim that I ended up getting probably half of my TP’s from that pilgrimage alone.
Having done that, and learned the joys of mining along the way (which is almost best solo), I decided I wanted the rest of them. PE doesn’t really have a “mission” system (except for the recently added beacons), so collecting TP’s became a self-defined mission. It gave me a destination to head for while hunting and mining. Also, you never know what advantages an area or town holds until you’ve been there.
Collecting TP’s in a team can be problematic. At first my wife and I worked at collecting them together, but we soon ran into a snag: dying and getting sent to the closest rivival terminal. This is how it would usually go. We’d start out from the same place, heading for the next TP, and we’d both mine along the way (trying not to step on each others’ claims). One of us would find something, let’s say me for the sake of discussion. My wife would go off to hunt to keep herself occupied while I drilled my claim. Sometimes she’d die. That would take her to the nearest revival terminal which could be a few km away. If it was a TP or outpost we had already visited, I would generally mine and hunt where I was and wait for her (or backtrack if she ran into trouble). But if she TP’d to the NEXT revival terminal, we were pretty much seperated. I was nowhere near a TP for her to get back to me, and I didn’t have the TP she was at. At that point, we’d disband the team and I’d continue on to the destination she had already reached. I guess I could have simply let myself get killed by the same mob that got her, so as to join up with her, but just out of principle I had to get to the next TP the hard way. And if I died, it couldn’t be deliberate. Since this was a “mission” in a way, I guess I felt I needed to “earn” the TP. This is not meant to imply that I didn’t get to a lot of TP’s by jumping on the pain train: I just didn’t do it deliberately.
So (in summary), as Rotten Ice said, collecting TP’s is mostly just “something to do” and makes it easier to meet up with people later on. Collecting with a team has its advantages and disadvantages. It is fun (and safer) to explore with others, but it’s also very easy to get seperated, unless you’re willing to sacrifice yourself to the god of travel–and if you’re not as uptight as I am, that’s a simple solution. 
If you go solo, I highly recommend taking up mining as a hobby along the way. If you have no armor, no weapons, and no means for obtaining mining equipment, then I’d say the provincial life can be rewarding too. 
-Gryffon
