As a result, Roddenberry's heirs since the days of The Next Generation have struggled to find ways to break the damn thing. The transporters won't work at warp speeds (except when they do). The transporters won't work through shields (except when they do). The transporters are sabotaged or disabled constantly by villains. The transporters have all sorts of frequently-abused limitations that are not really necessary except to keep them from being too powerful for the good of the story; for instance, why is it possible to disassemble living organisms and reassemble them elsewhere, but not to replicate life by assembling the same patterns out of “raw” constituents?
Surgeries of any kind should be completely unnecessary, so why was Captain Picard's chest cracked open to replace his artificial heart?
Babies ought to be delivered routinely via transporter. To its credit Deep Space Nine actually did feature something like this in one episode, and I'm sure that many mothers would still choose the traditional method at any rate, but it would be nice to hear more about transporter delivery from time-to-time.
The existence of “bio-filters” as part of the transporter system implies the end of all infectious disease, contrary to what is presented in many episodes.
How many shots of Starfleet personnel running down corridors, responding to some emergency, have we seen? Site-to-site transport ought to be routine in combat situations.
Why are security officers risked in confrontations with dangerous persons? Why do we hear “beam him to the brig” so seldom?
Wouldn't people, whether soldiers or civilians, carry something like a panic button that would immediately remove them from dangerous situations they may encounter? Forget about talking to some transporter operator and requesting to beam up, I'd like to have a global network of transporters tasked at all times to take you elsewhere, just activate something in your pocket or wherever. That would be a service I'd pay for!
Beaming food into the stomach, for people with very demanding schedules.
Getting dressed or undressed, for the same reason.
Skydiving without a parachute, only to be rescued by a last-second transport, ought to be a popular stunt.
Finally, consider the fan-favorite question of how exactly Seven-of-Nine goes to the bathroom in her one-piece outfit—I think you know where this is going!