Let's not forget that ST prose fiction first came into its own during a period when there was no onscreen Trek (except a Saturday morning cartoon that not everybody took seriously or paid attention to) for a whole decade. Heck, let's not forget that Star Trek didn't even become hugely popular until after it was cancelled. It was the constant reruns, not the original network run, that imprinted it upon the national consciousness. And when people clamored for more, books were one of the few ways to get it.
It is true that the books became more successful and frequent once ST was back on the big screen, and then even more so when it was back on TV again. So there is some correlation between the popularity of the screen franchise and the success of the books. But history shows that Trek books can be successful to at least a moderate degree in the absence of new onscreen Trek.
Why would they? Everyone's saying it's a good idea to have books in both timelines. What better way to differentiate them clearly for buyers than to use the TOS cast on TOS book covers and the Abramsverse cast on Abramsverse book covers?
See my comments above. Yes, popularity of onscreen Trek amplifies the popularity of the books. But the absence of onscreen Trek keeps the books popular among a smaller, more hardcore segment of the fanbase, because the books (counting comics) then become their primary source of new Trek. So even if the books lose that extra boost of broader popularity that comes with a successful screen franchise, that doesn't mean the core audience is going to abandon the books.
then let's pretend I didn't write "below". *grumbles about quantum theory* 
