Star Trek's "continuity" has only been an illusion anyway. Of the franchise's first forty years, every series could have existed as standalone with the exceptions of DS9 and Enterprise, which did draw from the Trek mythos, and ironically they were the two series from the first forty years that made the least splash amongst general audiences, and are at times viewed, not entirely inaccurately as the redheaded stepchildren of the franchise. Indeed, Trek Lore didn't start being tapped for story potential until around 2003 when the novels were really starting to be allowed to do their own thing, and then in 2004 when Enterprise did its fanwank final season.The best example I can think of a strong and enduring TV franchise is probably Star Trek. It's been going since the '60s, just like the Fantastic Four, Spider-Man and the X-Men! I think if Star Trek is going to continue to exist as a TV show it should probably look back at Star Trek and treat its continuity the way Star Trek does.
Indeed, look at the franchise's popular points in the first forty years, on TV that's TOS and TNG. And why are they so popular? Because they're the sort of show the casual viewer can sit down and enjoy it without any foreknowledge. The most popular movies from that time period? TWOK and TVH. Yes, TWOK is a sequel to an episode of TOS, but it works just fine if you hadn't seen that episode. And need I point out, the movie contradicts the episode it follows up on, yet that doesn't prevent anyone from considering it amongst the best. And TVH? That's basically a comedy set in the contemporary era that has little connection to the Star Trek world, and that ended up being the franchise's biggest box office hit before Trek XI came out.
Bottom line, Star Trek's continuity is not the selling point some fans seem to think it is.
Ah, what? Doctor Who is notoriously anti-continuity. One of its most revered writers/producers is quoted saying "continuity is only whatever I can remember." Indeed, during the period he was involved with the show, time travel was actually removed from the show, the Doctor was stranded on a vaguely defined "near future" Earth, which the show couldn't even stay consistent about when that "near future" was to the point that it ended up becoming the present day the show was made in at one point, only to be contradicted even further. And since time travel was removed from the show at this point, you can't even use the "time war, changing timeline" excuse many try to use to explain Doctor Who's inconsistencies.Doctor Who has done incredibly well in that respect, too. Continuity issues here and there, but they have a time war to explain some of that. Useful things those temporal conflicts.
And even that can only be applied to the period of 2010-2017, the Steven Moffat era, which is the only time in the show's history that Doctor Who was actually about time travel and the implications and consequences that go with it. Before and since, time travel has only been a mode of transport for Doctor Who.