I don't personally agree with the model of the latest dlc making the rest of the game irrelevant, but again (using d1 as an example), they'd miss out on maybe the first raid and set of light levels, but would still experience the same story and continue onto the next batch.
I don't seriously think that doing the same raids/nightfalls for 5 months* is "missing out" (and I played destiny all through TTK).
*Arbitrary number, I don't actually remember the length between expacs
And arguably, vanilla was the weakest point of the game in my opinion, that is.