To me this has already been answered, and it doesn't require the obligatory "alternate universe" fan theories.
In order to safely jump any significant distances or with any significant frequency / accuracy, you require a Tardigrade. Either a Tardigrade itself must navigate the network, or a human (like Stamets) infused with Tardigrade DNA. There is no other way to make it work.
So....
1. The Tardigrade may have been sentient...so that's a no-go for the future. Can't just capture one and enslave it to make a drive system work.
2. The Tardigrade found it's way onto the Glenn because of the way they were storing their mushrooms. It was a fluke. We're not likely to ever see a Tardigrade again, and even if we do, it's obviously extremely dangerous if provoked and not properly contained.
3. And even if we did see one again, genetic manipulation is illegal, so unless they want to be slave navigators, which I doubt, you can't do what Stamets did and make other navigators.
4. But ultimately we know we DON'T see one again, because there's never any mention of the drive later in the continuity of Star Trek.
Bottom line: Tardigrades are a key component. And due to the fact that they ain't never coming back...the drive is dead unless one person in the entire universe (Stamets) is agreeing to use it on a ship that is properly outfitted to employ it.
Problem solved. No need for inane fan theories or foolish in-universe arcs.