aslanov, I agree w. you about the many beautiful Schumann melodies.
The concerto's last movement is quite nice -- it soars, though my favorite part is the second theme of the opening movement. Schumann uses lots of syncopation (almost "ska-like" at times), maybe a bit much, but at least it's a distinguishing characteristic.
I, too, form my own tastes, though I'm very grateful to my (long deceased) main teacher, who exposed me to a broad range from all periods, but not much Schumann (except Kinderscenen and Sonata #3). I decided to learn Toccata, Carnaval, Symphonic Etudes, and Fantasy on my own in my 20's after ceasing taking lessons. But as stated in some other threads, I'm thinking about and welcoming suggestions for Alkan. People seem to have similarly strong opinions about him too (and about his prominent proponent Marc Hamelin) -- some he's stupendously great, others that he's essentially sound and fury signifying nothing. I guess everyone has their opinions, and people can state their reasons, or not, that's their prerogative. I guess it's the music that draws no reaction whatsoever (like, "oh that's OK") that probably isn't going to be around for long, more than the pieces people love or hate.
One thing about whether pieces are overrecorded (which I agree the Schumann concerto is, but I disagree with the speculative reasons some have given). I'm just glad if people listen to it or classical music at all -- so few people have heard any of these pieces, even the warhorses, even once unless they're part of TV commercials or movies (which I don't think much Schumann is). Just the other day, a college student was very eager to get started listening to classical music, so I must have given him over a hundred recommendations from all periods. I had chosen Carnaval as the Schumann piece but just added the Piano Concerto

It was refreshing to see a young person spontaneously ask to be introduced to classical music. Some people hate opera too (not me, I love it, and also really like piano pieces based on operas, like Liszt's fantasies on Norma, Rigoletto, or Don Juan, or Thalberg's on Don Pasquale).
BTW, any tie between your screen name and the C.S. Lewis characterAslan?
David