There's also an admission of this sentiment in the foreword of Faiz's Zindaannama by Major Ishaq, one of his co-accused in the 1951 case: that Faiz's poetry still had to make the leap from the drawing rooms to the streets.
That said, it isn't as if it never did: there isn't any political party, including the right-wing ones, that haven't co-opted his poetry, much as the state has co-opted Iqbal's, into their sloganeering and banners. The hard left parties (not the much-maligned mainstream "liberal" ones) do so to this day, and their lack of penetration in the masses notwithstanding, they are proletarian and can't be accused of being consigned to supposedly liberal drawing rooms.
Speaking of hard left, there's something to be said about ideology limiting his appeal vis-a-vis Iqbal: one can try, and many have, to apply benign labels such as "humanistic" to his poetry in order to downplay his lifelong commitment to communism, but since communism never caught on in Pakistan, its leading literary voice will always come off worse off when contrasted with the official national poet professing an altogether different ideology. I say this without in any way disparaging either (poet).
Whether this alone explains the disparity in popularity, I don't know. My late college Urdu professor, a great influence on me, listed Mir, Ghalib, Iqbal and Faiz as the respective poetic giants of four different eras in the Muslim history of the subcontinent: pre-Raj, post-1857, pre-1947 and post-1947. Or 18th century, 19th century, pre-independence 20th century and post-independence 20th century if you will. It should be possible to appreciate both Iqbal and Faiz without denigrating either. I certainly do.