Is that really true? I thought they were always trying to get the general audience. They always actioned up the movies compared to the TV show. And they did the Kirk meeting Picard plot that seems popular to the general audience. Then there are things they didn't do which fans might have wanted, such as Voyager having continuity and Nemesis / Enterprise not sucking. And those ideas probably aren't unappealing to the general audience either.
But did they go too far in those regards, sure you want to appeal to a wide an audiance as possible, but at the same time you don't want to alienate your core audiance, if your core audiance is critising a show/film that might rub off on the more general audiance, if even the fans don't like it then it's unlikely I will.
I feel like those shows did plenty of pandering to those who weren't fans. Tsunkatse anyone?
And seriously, at one time there was a fan base of like 20 million watching TNG. Most of those fans left because it just wasn't as entertaining, not because there was fan pandering. The only real pandering probably happened in the 4th season of Enterprise, and by then, the prime timeline was already screwed.
Tsunkatse pandered to a different fan base not to a broader audience. And it was the exception, not the rule.
What did Voyager actually do to grow the fanbase? The Next Generation was a pretty cutting age show for the late eighties. However, Voyager just kept fetishing that model of storytelling into the twenty-first century. It added a sexually objectified female character, but that was pandering to what it perceived to be the target market - nerds who like boobs. I love Jeri Ryan's performance, and like her character arc, but the addition of Seven as the new focus character was the point at which it was clear this was not a show that saw itself aiming towards a broad audience, but towards shut-ins who think "sexy" is a painted-on catsuit.
(Whatever about the infamous "male gaze" scene in Into Darkness, it was a single short scene, and had an accompanying "female gaze" scene with Khan in the shower that was unfortunately cut.)
By the time that the first two seasons of Enterprise had committed to doing "what TNG had defined as Star Trek stuff" with "awkward sexy stuff because nerds like boob, right?", the franchise was terminal.