The OP asks, “Why is only Chabad very into Moshiach?”
The answer is that the question is based on a false premise.
All those who follow true Judaism, are also “into Moshiach”, however they differ in approach.
Should all Jews be begging G-d to send the Messiah? Yes. Religious Jews pray for this thrice daily.
Should we put more feeling into these prayers? Yes. We should always make our prayers more sincere and heartfelt.
Should all Jews be making special programs and events (for example, like in MetLife Stadium) for bringing Moshiach? The answer is that if we knew that this is what’s holding up the coming of the Messiah, we would surely do so. However the notion that the making of Moshiach rallies will hasten his coming; is debatable.
The idea of hastening the Messiah’s revelation, is dealt with here
Do we have to bring Mashiach?
I note there, that:
We see that there has been a long standing debate regarding the
question of, is action required on our part to help bring the future
redemption. Those rabbis that believe that we need to take an active
role in creating the messianic era, are echoing Rav Kook’s position.
It is interesting to note the “well known” (6th) Lubavitcher rebbe’s
position, as quoted by Rabbi Shulman, which advocated a more passive
approach. Contrast this with the current Lubavitcher approach, which
is to attempt to hasten the final redemption, and their mission is
centered on this goal.
When Rabbi M.M. Schneerson was alive, there was a strong movement in Lubavitch to recognize him as the Jewish Messiah. The debate whether or not Rabbi Schneerson himself hinted to his alleged status, or if it was merely his followers who proclaimed so, is moot. The point is, that the lives of Lubavitchers revolved around a Messianic culture, and they believed that the Rebbe’s “coming” was imminent, and all they needed to do was help hasten his revelation. Which is why at the time, Lubavitch was “very into Moshiach”, since they felt that the Rebbe was counting on them to make it happen.
After Rabbi M.M. Schneerson’s passing, most Torah Jews recognized that he isn’t the Jewish Messiah, since the potential Messiah is a live human, living among us today.
Also, the Hebrew Bible makes NO mention about the Messiah failing to fulfill ALL the essential Messianic passages, and will have to return in the future to do so. If an individual fails to fulfill even one of these conditions, then he cannot have been the Messiah, which is why Torah Jews can never accept the Messiahship of any personality, however noble or well-intended, who died without ushering in the age of physical redemption.
Those who continue to insist that Rabbi M.M. Schneerson is the Messiah, are regarded as a breakaway Messianic sect, and are therefore shunned by mainstream Judaism.