His clipped, terse prose makes him very readable, and in a way the exposition also works in his favour - this is a literature of ideas after all, and whether or not you agree with them or the way they are put forward, Heinlein at his best generates a remarkable number of ideas per page. Why is he so popular then? Well, I'd say that his fame was sparked off by the Future History tales - certainly one of the strongest bodies of work in SF at the time - and carried on form that momentum.
Stranger in a Strange Land, which could have been a fascinating tale of culture shock amplified, became a sermon on Heinlein's own version of the 60's creed. Starship Troopers is making the case for a militarist meritocracy - what little plot there is, works around this, instead of the plot driving home the message.
I think what rankles is that a lot of it seems preachy, rather than suggestive, as is the case in, say, Frank Herbert's work. I've been revisiting Henlein lately, and its true that he is very expository.
