There might be a generation/region/country gap here, but as a 51 YO Australian who's played with 3 main groups since 1990 and was part of a Uni roleplaying club, I've never been in a group that only played D&D except for a year or so in high school - and that was just one campaign.
To me, this advice is entirely reasonable.

When the current campaign ends you say to your group "Hi folks, I'm happy to run the next game. I've got an Idea for a Fate game set in a universe where anthopomophic animals all live on different planets. The party start as..."
Anyone else wanting to run something put forward their offering and a decision is made.
The last "game start up" I was involved with was when a friend offered a group that included one mutual friend and one who has played a bit in the past but not with anyone I know.
He offered 5th ed D&D, a post apocalyptic mutant game, an Ars Magic apprentices game and a few other options.

So a change of game normally requires you to sit behind the screen, at least until your group are used to trying different games, then you might get someone else to agree to run the one you really want.