Everything you say is true. Fallout is a storyfag game through and through - anyone seeking great combat and exploration need not apply.
It's been said on here before, but Fallout's greatness comes from the way it's arguably the first ever RPG where it feels like you're actually playing against a DM who's reacting to what you do. Successfully creating that illusion is at the core of any story-based RPG, and Fallout is one of the only games ever to succeed at it. You classify this as "entertainment elements", which comes across as kind of dismissive. It's fair to criticise Fallout's core mechanics (because they are a bit shit, for the reasons you pointed out), but it's equally fair to say that the game doesn't necessarily need great combat. And at least the combat is serviceable, rewards/punishes you for your skill point allocations as it should, and is over quickly. It's not like New Vegas, which might be the best Fallout game if it weren't trapped in the fucking Gamebryo engine, forcing you to endure the worst combat known to mankind.
Fallout's story and setting are also wrapped up in such a great package - the graphics are beautiful, the music is amazing (even if it's just a dark ambient CD which Mark Morgan found and decided to copy every fucking track off), the clay models for the talking heads all ooze character, boosted by top voice acting. You correctly mention these as the things people remember about the game, but again, they're such a success that they're all the game needs to be great. It's not a perfect game, but it sort of shows you the outline of a perfect game, which is more than most RPGs do.
Fallout's briefness is also part of its strength. Fallout 2 and New Vegas are both great games with their own strengths, but their length isn't one of them. Unless you just do the main quests in both and ignore 95% of the content, 2 and NV are utterly overlong and by the end you're just begging for it to end. Fallout 1, meanwhile, throws you into a snapshot of a fascinating world, shows you a glimpse of the lives of the people living there, sends you on a journey with a clear beginning and end, and concludes at the perfect point, where you've seen enough to be deeply invested in the world, but seen so little that you're wishing for more and your imagination is running wild.