Learning to appreciate Babbitt's music (or 20thC music as well)

I’ve been wondering..
All those pieces of 20thC music we’ve explored so far (eg. Babbitt, Berg, Ravel, Messiaen, Schoenberg, etc.), they seem to be crafted in such an intellectual and mathematical way and it is really quite exciting when we discover these compositional strategies. Does it mean that the way we appreciate these pieces of music should also be from an intellectual perspective as well? The reason why I say this is also because these pieces of music are not those that our ears are accustomed to listening or the conventional sit-back-relax-and-enjoy type (like FM92.4 would say it).

Referring specifically to Babbitt’s music, Andrew Mead (1994) says that we must be able to follow the music’s structure in order to fully appreciate it. This is because “the strong emotional and expressive charge of his music is deeply rooted in the ways notes and rhythms work together to create webs of association and connection over ever-larger spans of time.” I was quite pleasantly surprised that Mead or anyone else would describe these music with phrases like ‘strongly emotional’ and ‘sensuous beauty’. Previously, I only thought that music by Chopin, Liszt or their contemporaries could be described as such, but not anymore. This new perspective opened up for me another set of ears when listening to 20thC music.