I’m not an expert on this topic but here’s my 2 cents. First, Rebbe Nachman specifically told his followers to come to his kever on Rosh HaShana. Second, he also wrote (Likutei Morahan 2:109) that the graves of tzaddikim have the kedushah of eretz yisroel (“mamash” he added). It’s not surprising that non-Breslover rabbonim would rule that it is forbidden to go to Uman on Rosh HaShana (as many Israeli rabbis have). But when a great tzaddik says to do something, and you follow that tzaddik, you can and should do it.
It’s true that many people who go are not full-fledged Breslov chassidim, but nearly all of them are inspired to some degree by Breslov chassidus (for example, many are BTs or on the road to becoming BTs in part because of studying Rebbe Nachman’s works).
Also, many people who go find that it makes a huge difference in their lives. This includes women who go at other (non-Rosh HaShana times). Interestingly, though, there is apparently a small proportion of Breslov chassidim in Israel who do not believe in going to Uman — but I’m not sure who they are and what their reasoning is.
Sure, people could have spent the money on tzedakah instead. But you can say that about a bunch of things — siyum hashas, eating at restaurants, going on vacation, pesach hotels, etc.