This kept me awake thinking about it... So that's a very plausible real world possibility, by changing the probability of the person being at point B, apposed to point A. The problem is, that doesn't jive with the canon transporters workings, mainly the buffers, and slow fade, which imply that the person is being "deconstructed", converted into data and temporarily stored somewhere, transmitted, then "reassembled", presumably inside some force-field that empties the space they intend to beam too.
I know. I've noodled that. Best I've come up with is a sort of "time delay" that got added after earlier models. Something that holds the transportee in quantum stasis -- enforced indeterminacy, but as an isolated event-mass -- to give time to re-verify the destination point or otherwise prepare it. That could even possibly be a later-discovered effect/use of the Heisenberg compensators. I can see it originally being a realtime thing -- as the person fades out on the pad, they're fading in at the destination. I can also see how that could have resulted in some unfortunate incidents when conditions changed suddenly during transport. So things like the confinement beam, the time-delay, the scanning and mapping of the transportee as a safety backup... One thing and another leading to the systemry we're familiar with -- just functioning differently from originally posited. I originally stumbled across explanations of what's going on at the subatomic level while looking into something else, and the lingering bright motes in transport could even be those short-lived virtual photons I had been digging into -- the things that make lightsabers so bright, but unable to light up a room.
Point is, mainly, that that's a thing we or others could come up with something for fairly easily. It solves the preservation-of-mass issues episodes like "Enemy Within", "Second Chances", and "Rascals" create. And it solves the problem that, even if the force fields are incredibly robust, we don't
see trillions upon trillions of nuclear bombs' worth of energy being contained by them as someone is beamed out. Which is what is required to break subatomic bonds. We have hundreds of trillions of cells in our bodies. Never mind organelles and cytoplasm, each has a nucleus containing a full set of DNA, each strand a molecule a hundred million atoms long. Just like breaking the speed of light, it is not a brute-force problem to be solved. Rather than create infinite energy to overcome infinite mass as one crosses the threshold... HA! We simply compress spacetime in front of the ship and expand it again behind, "pulling" the universe past the ship, in effect. Phasers became possible with the discovery of subspace, as the amount of energy released by something being disintegrated is being shunted
somewhere -- otherwise, again, trillions upon trillions of nuclear bombs' worth of energy released as each of those subatomic bonds is broken.
Even something as "simple" as the communicator... Yes, they inspired cell phones, but they are not cell phones. They are FTL-boosted satellite phones, with biomonitor functions and other subtle bells and whistles. By TNG, all that -- and the power to run it -- is compressed into the insignia pin on the uniform. Even something as seemingly familiar as the computers use holographic memory, optical data transfer, synthetic neural networks, and subspace boosters to run faster than light.
Whatever transporters do, it is that kind of circumventing-Newton finesse, not trying to match immovable object with irresistible force. Post-Newton, post-Einstein, post-Hawking, Star Trek is showing us controlled manipulation of the substance of reality as everyday tech.