Near instataneous travel is horrid for star trek.
It destroys the idea that the crew is all alone on the edge of known space. Why get caught up in a ship if logically anyone can come in and save the day in an instant.
It makes no sense for captains to have as much power as they do if obviously there must be a admiral in subspace range.
World building of trek has far less value if Klingons vulcans insert species all live directly beside earth. The idea of seeing the undiscovered or the next frontier really has value when no one has ever been to that location.
This doesn't apply because it's sci fi, it applies even if we were talking about something that is strickly fantasy.
Imagine Lord of the Rings if they could of walked to the vulcanoe in an hour.
Why? Why is FTL travel "horrid?" What is the alternative and its benefits to the story and/or world building?
I still don't understand the point because Star Trek has always operated at the speed of the plot (Warp 10, anyone?) and simply requires more consistency to make it feel more "real"
Star Trek has not really treated space as "big" so much as it has treated it as complicated. There are political boundaries, various species with their interests, worlds that don't have warp drive, etc. When they travel to a system, there is as much political discussion and considerations as there are speed ones.
Finally, your Lord of the Rings point is an oft lamented facet of the lore that is misunderstood. The Eagles have their own politics and generally remain outside the affairs of men. Secondly, even they could walk the volcano in an hour, there are still
armies (i.e. political forces) at work to stop them.
Just because you can get there fast doesn't mean the journey is less interesting or has less obstacles.