The thing with GoT is that the books - themselves gripping, and at times, extraordinarily good - had already made this world familiar to a vast potential audience, and thus, an audience was primed to see how this story might translate to the screen (extraordinarily well. by all accounts).
This is not the same with a 'new world' - of unfamiliar characters - to the ST franchise in a new series, especially as the last one "Enterprise" was so.....underwhelming.
Actually according to several things I've read, GOT was a bit of a gamble (regardless of the relative popularity of the books). A fantasy show, with dragons, a niche genre (even with the success of the LOTRs movies), and a huge budget, serialized, on a cable channel. S1 to S7 the viewers increased by a factor of 5, that's huge, and it shows it took some time to ramp up to the now record breaking viewership.
... but, as someone pointed out, it had a massive advantage being on a premium channel, that offers movies, docs, some of the best original programming over the years (Sopranos, The Wire, 6 Feet Under, Curb Your Enthusiasm, Veep), it makes the subscription decision easier vs. effectively, one show for the monthly (even if per episode is not really that expensive).
For a new Star Trek series to gain momentum, it would have to be on a network with some compelling, existing programming (HBO, SHO, FX, AMC) or a service with enough breadth of offerings, the price is way more palatable (Hulu, Netflix, Amazon). I feel like the show is going to fail, regardless of how decent it is (though with it currently under review embargo, I don't have high hopes for the quality either ....)