Since it's known that you can't ride flat out for anything but a short bike race, teams make sense to me. Despite rules against working together in early tours, it became evident that riders were going to work together in groups. So eventually allowing teams made it somewhat more fair by making certain that some riders don't get disadvantaged by not having someone to work with.
As well, understanding some of the physical limitations and other factors behind the strategies during the tours and grand tours does make things more interesting to me. It's not just a strategy of winning every stage of a tour, because you don't have to win any to be the overall GC winner. And you can realize that different teams have different goals. Quite a few teams have no real chance to win the overall GC so they work toward other goals. Sometimes their successes at their goals can cause some interesting complications for the teams that do have a shot at it.
When you can realize all the different races going on within a stage of a tour or grand tour and see how the teams going for the overall GC can make or break themselves by getting caught up in those frays, it adds more to the interest for me. I have to say that the short one day races that you can ride all out and are over in a little bit of time just don't appeal to me nor do I understand them.