Well, I'm generally a person who just goes along with stuff on TV (as long as it's fairly self-consistent) and I think I'm pretty good at suspending my disbelief for about everything fictional
Well, nothing wrong with that!

I'm usual prone for overthinking stuff in fiction. Which is a very usefull skill in real life, but sometimes takes the fun out of entertainment when you notice Cpt. America's shield works one way in a scene (absorbing energy) and completely different in another (reflecting said energy). Or the multiple size/weight issues in Ant-Man.
Would you mind laying some out for me? I haven't really been in this particular discussion before, so I'm fairly clueless
Since this discussion has already moved on several pages, I just want to point you to this great summation from
@eschaton:
Not galaxy spanning - multiverse spanning. This was one of the greatest problems with it as a concept.
I mean, spaceborne fungus I can understand as a concept. I'm not exactly clear on what - presuming they are detrivores like earth fungi - they're eating, but subspace is a mysterious place, and we've had things like giant space amoebas before. So it's no big deal.
But as the first season continued on, the space fungus linked every single point in the universe. Also every single point in time, and every point in every possible other universe in the multiverse. This must mean there is a single linked fungal entity which is itself larger than our entire universe. Further, the series strongly hinted that it was either self-aware in some sense or the souls of the dead resided there.
If something is technologically possible, it will eventually become invented, and even become widespread. The problem is even worse considering the mycelial network connects every single universe and every point in time. Given that is the case, there are an infinite number of other alien races - some of which will, at some point in their history, explore the spore drive. Hence it is a certainty that there would be numerous incursions throughout history from other universes and time periods into Trek's present.
That covers a lot of it.

And he didn't even mention the entire universe can be destroyed through the funghi with only one, single(!) ship at one point in time!
One of my additional main problems is the human DNA-thing, where Stamets can use that thing because humans share DNA with Funghi - indicating either Earth-origin or, more likely, that somebody has
no idea what DNA actually is or does. But in any way, it implies that "the mushroom" is the single biggest and most important being in the multiverse - in fact, that MOST OF REALITY ITSELF is actually this giant funghi - and the entire universe as we know it (+a lot more) is just something between his roots. Which just leaves
so many more questions, like what's the meta-level where the Funghi got his energy from and such and why, if Tardigrades can travel on it's root, they haven't overtaken Earth a long time ago.
It's just such an enourmous retcon of what the Trek universe
actually is. It's not comparable to other goofy stuff like the Travelers "The universe is just built upon thought" - which
actually might even have a kernel of truth in it - with Quantum physics actually being dependant on observers, and thus there are probably methods to alter reality we can't currently imagine.
To be fair topwards the show, I have to say while the concept of the mushroom itself is absolutely bonkers, I absolutely like
how they treated it on the show. When Stamets explained what it is, he did so in a very science-y/matter of fact-way, and so far the mycellium network istself hasn't been treates as something godlike/the Force/esotheric Hippie mumbo-jumbo - but as if it were something scientfic, logical that humans can used. That is usually my only demand on "science" in Star Trek - because that ain't gonna' be realistic anyway.
This leaves me in the weird situation where I think the concept of a ship that can instantanious travel (like BSGs jump drive) is actually pretty interesting in the Trek universe (despite the canon concerns like why Voyager didn't use it once), and I like how they used it on the show (loved the hundreds of jumps in the midseason finale) - even if I think they could get more out of it than they did. But that I find the
explanation for said drive - the boring exposition that actually nobody pays attention to normally - so abstruse cringeworthy, it diminishes my enjoyment of the entire show a little.
That's why I'm absolutey with Eschaton in how I would like to continue this storyline:
Of course, Discovery is far from the first Trek that has treated technology less as a natural progression from the development of civilization than a series of plot devices that can be forgotten as needed. That doesn't mean that it's something that should be continued however. It would be best if DIS eventually finds some way to "kill" the drive outright - cauterizing the ability to use it from our universe entirely.
It's absolutely impossible to just "forbid" the use of the spore drive, that would absolutely break continuity in the Trek universe. But at the same time, it would be a grave mistake to "kill" the mushroom network itself: It would "fit" with continuity. But on the other hand, it would imply humans killed the biggest, largest, most important living being in the entire multiiverse. Which is
not something I want my heroes do on Star Trek.
The best possible solution would probably the mushroom itself would just cut himself off from the multiverse and be not accessable anymore. And then, for all intents and purposes, the writers should simply
forget about it for future stories, like Trek has forgotten other super technologies as well (the Dyson sphere from TNG, or VOY's many slipstream versions).