The general stereotype of classical music being boring is very wrong. You just have to be able to understand what the music is trying to show you. These composers make that easy.
I completely agree that the cliché about classical music is wrong. It is not boring and to the composers you mentioned I would add Mahler. Prokofiev and even Beethoven, Brahms, Stravinsky, Rachmaninoff, Scriabin.
Now on the idea that classical music isn't for everyone, I'm not sure I agree with that. Although I'm sure that wasn't your intention but I feel like there's often an elitist mentality hiding behind this statement. What I do believe is that classical music takes effort, patience and curiosity to appreciate and that's what turns people off without them knowing it. It's very difficult to enjoy a 40-min long symphony or concerto if one doesn't know sonata form or doesn't have minimal knowledge about the history of music and composers. But that's something that can easily be grasped with a little effort. Also, from my personal experience, it takes time and repetition to appreciate a piece, and that by actively and curiously listening to it several times. In order to appreciate a piece, you need to get familiar with the material and the structure. The more you listen to it the more you discover things inside it and appreciate it. And while some composers and works are more accessible than others, classical works are more complex than other genres generally speaking in terms of form, counterpoint and orchestration and from the romantic era onwards in terms of harmony as well. There's a piece I've been loving recently: Prokofiev's 7th sonata. I heard it about a year ago but it didn't really speak to me at first. I thought it was just noise. I also shared it with one of my friends who doesn't really listen to classical music, and he also told me it felt like random noise. I didn't immediately appreciate it but after a few tries I'm absolutely IN LOVE with it. I couldn't appreciate it ago because my ear wasn't used to hearing that much dissonance and harmonic instability. But now that I'm a bit more used to that, I'm able to understand it musically and appreciate it.
One last reason is that people don't really have the time to listen to a Mahler symphony for example. All Mahler aficionados will tell you that the effect is maximized if you struggle through the whole symphony and reach the finale. But Mahler's 2nd symphony is an hour and a half long. Who has the time for that in this fast-paced world?
On the other hand I truly believe that classical music is so rich it has something for everyone. People tend to think of classical music as one genre, but it's actually a cluster of musical periods and genres. The difference between Mozart and Prokofiev is huge, same as the difference between a symphony and a prelude or a lied (which is basically a song).
Bach – Chaconne from Partita No. 2 in D minor (BWV 1004)
Beethoven – Violin Concerto in D major, Op. 61
Sibelius – Violin Concerto in D minor, Op. 47
.Karol Szymanowski – Violin Concerto No. 1, Op. 35
Erich Wolfgang Korngold – Violin Concerto in D major, Op. 35
Paul Hindemith – Violin Sonata in E (1935