Chassidus has already accomplished much of what it set out to do, and has caused significant changes in the "mainstream" of yesteryear, such that the non-Chassidism of today is really a product of both the "mainstream" of yesteryear, and Chassidus itself.
Warning: Serious over-simplifications below.
While it is true that Chassidus has changed quite a bit from it's origins, I disagree that Chassidus has returned to the ways and practices that it originally broke from.
As mochin rechavim's answer correctly points out, one of the main points of Chassidus was to break away from the idea that the only way to serve G-d properly was to be a Talmid Chocham, and if you weren't, you were a nothing. This was simply the metzius of how simple Jews were viewed back then. If a Jew couldn't learn Torah, then he was viewed as inferior. In addition, if a Jew didn't learn Torah, or didn't do mitzvos, he was considered completely lost to Judaism. I don't mean halachically, I mean in the public perception.
Now, as everyone knows, Torah learning is incredibly vital to Jewish life (and learning ;-)). (Toras HaChassidus itself is Torah of the deepest and most profound kind.) But this does not mean that it is the only way to connect to G-d. Chassidus taught (and teaches) that the Jew is innately connected to G-d, and is precious to G-d no matter what. This had (and has) the effect of: 1) causing the Jew to feel closer to G-d, and to therefore act in such a way, and 2) removing sadness and depression from the Jew, and replacing it with joy. (As is known, the Besht and other Chassidic masters placed much emphasis on serving G-d with joy.)
So this was one of the things that Chassidus set out to accomplish (and was incredibly successful at, I believe): to change that perceived inferiority of the simple Jew. This was necessary in two ways: 1) to change the community's perception of unlearned Jews, and 2) to change the unlearned Jew's perception of himself.
In this respect, Chassidus was incredibly successful. Look around today to see how much.
Also, Chassidus also introduced Toras Hachassidus, a new dimension in learning and understanding G-d and his Torah. This is certainly still studied today.
As far as breaking away from "the excessive legalism and stringency that dominated Ashkenazi Jewry", I'd say that Chassidus wanted something more.
Chassidus injected an idea of connection and closeness to G-d that (I believe) did not exist before. It tried to show that observing halacha by rote is, at best, half the picture. It was at least equally important to think about the One who you're learning about, or praying to, as it was to learn and pray in the first place. This is not to say that Chassidus advocated (or advocates) anything less than what halacha requires. But it tried to bring back the life into it's observance. Chassidus wanted to make Jewish practice more G-d-conscious.
I'd say that Chassidus has been successful at this, and is continuing to try to bring this into the public consciousness.
Has Chassidus moved back more into the "mainstream" from when it first started? Yes. This is a result of both Chassidus moving towards the "mainstream", but also, and perhaps more importantly, of the "mainstream" moving towards Chassidus.
I'd compare this to the Rambam's dictum: When you want to change a flaw, move to the opposite extreme. Then, once you've become accustomed to that, you will be able to move toward the middle.
Also, as mochin recahvim said, every generation needs something else, and this is what this generation needs. What was necessary for yesteryear's generation may no longer be necessary for our's. So while Toras HaChassidus and the fundamentals of it's practice and theology (for example "Chassid Sorfon") remain unchanged, some of the externals have changed.
This ended up a lot longer than I had originally intended, but what I've mentioned is really only a snippet of the larger effect of Chassidus.
For more information on this, I suggest listening or reading the beginning of "Inyana Shel Toras HaChassidus, available as an audio lecture (thanks @mochin rechavim) or Hebrew/English PDF. This is geared towards Toras HaChassidus (specifically as taught by Chabad), but starts from the Baal Shem Tov.
For a more general history of the time, and the effects that Chassidus hoped to have (and had), as well as the fundamentals (rather than the externals) of Chassidus, I very strongly suggest Rabbi Yossi Paltiel's Shiurim here. (Again, it's from the perspective of Chabad, but he goes through all the history.)