Well, to at least one interpretation of WTH the warp bubble is. By the time of voyager it no longer sounds like a time-space distortion, but more like moving from normal space to subspace, whatever that is.
Yeah I never got why occasionally dialog and plot points sometimes treated subspace as... an alternate dimension or something.
But then Voyager had a severe problem with remembering its own technobabble. Like, you have the captain more than once order full impulse to some star that's stated to be several light years away. So, err, doesn't she mean go to warp? Does she want to get there in a few years? So they may have gotten the whole subspace thing mixed up too.
TNG did that a few times as well. On one occasions Picard ordered helm to go to Warp 3 and Helm responded "Aye Sir Maximum Impulse." I'm going to to a rare head cannon rewrite and just assume they were going to impulse to get out of the system before going to Warp. I'll ignore the fact that brings up even more problems.
And actually this address another common Warp/Impulse trope. The Shuttle Crafts. Now I know Star Trek wavered with enough regularity on this you could set an atomic clock by it but at least some (most) of the Shuttle Pods / Shuttle Craft where strictly impulse with things like the Runabouts / Captain Yacht's being the smallest warp ships we've seen. (And if some of the shuttle craft are Warp capable that begs the question you are putting a warp drive in a vessel I've never figured out where they fit anything since the interior space of those things seems to fill up the entire volume....).
But anyway all the time on TNG we had a crew member returning from Shore Leave or a Seminar or Bat'leth Tournament or whatever... in a shuttle craft.
Really think about the logistics and time frame on that and how little sense that makes.
Let's say you are traveling from Planet A to Planet B but on the trip you have to drop Crewman Timmy of on Planet C which is.... a light year detour off of the shortest distance between Planet's A and B.
You can't stay on your current course and just drop Crewman Timmy off in a Shuttle Craft 10 light years away. It will take him at least a year, probably more, to get there.
When you are traveling a several times light speed I can't really envision a scenario where dropping Crewman Timmy off "X Distance from his destination" where X distance is a distance that Crewman Timmy can reasonably travel in a sub-light ship that doesn't already put a FTL Ship... there. A distance you can travel in a few minutes is going to take months or years for them. There's just too much of a disparage in speed for this to make any sense.
I get that putting characters in situations where they are separate from the ship is just something have to be able to do for plot reasons but still.
I like one fan theory (that doesn't really work with what we see on screen and to be fair only works if you don't think about it too hard) was that some smaller craft didn't have full on Warp Engines but had Warp Field Substainers, so a ship travelling at warp could detach a shuttle and have the shuttle stay at warp (assuming at a constant speed) but couldn't actually accelerate to Warp Speed on their own. Tweak that idea around a little and it could almost work.
Or have it so that Shuttle Craft can operate at Warp but don't have actual engines but use... stored energy (Plasma or Fuel Cells or Techno-whatever-babble) like a battery instead of an engine so you have a shorter range.
Also if Trek could make up its mind if FTL movement is Newtonian or not that would be nifty.
That said, yes, that drive actually has more than one theoretical problem. Not the least being... well, remember the ST:TNG "New Ground" episode where they try to move a ship on soliton waves? And they realize mid-way through the experiment that the wave would obliterate the planet they were sending the ship to? Yeah, that's one of the possible problems of the Alcubierre Drive.
There was a version of this I liked on a thematic and plot level, the Mass Effects Relays from Mass Effect.
Ship's can't travel faster than light on their own in the Mass Effect universe but use Mass Relays, essentially giant almost moon sized railguns that can accelerate ships to FTL speeds. This means ships can only travel on specific routes which is an interesting idea on a plot level.