Still, the whole notion of being promoted from lieutenant to captain in a few days stretches credibility in the extreme.Yeah, that whole "transwarp beaming" thing was pure garbage. Nimoy was able to sell it to a certain degree, but even he could escape from that example of bad writing. Still, it wasn't as bad as Kirk's promotion from cadet to captain inside of a week. That was laughable.
I too enjoyed T:S somewhat more than Star Trek. The former was average, and the latter below average, for me.
Kirk wasn't actually just a Cadet. I read somewhere that the character had the rank of Lieutenant just like Spock was a full Commander.
Between two stationary points or from a stationary point to a ship traveling at warp? What about "matching warp velocities for transport?"Their long distance beaming was established as possible in Star Trek TNG, but it was rarely used due to the power cost. It was in the episode where Picard's "son" was kidnapped by the Ferengi.
In the face of massive casualties (both the loss of nearly the entire Academy class plus literally billions of potential officer candidates from Vulcan) coupled with a conflict apparently ramping up off screen, it is entirely reasonable to promote an officer several grades (a graduate of an officer academy is granted an officer rank immediately upon graduation) who has not only shown he can lead a crew the size of the Enterprise's, but do so extremely well while saving the capital of the nation.
In prior major conflicts, such as World Wars I & II and Vietnam, when units suffered extreme casualties in the field, until replacements could be trained and shipped overseas, junior officers were forced to step up into billets far above their pay grade, senior segreants commanding companies, for instance.
The US Navy, again for instance during WWII, also frequently appointed very young (age 25-30) men to command (hold the ship commader's billet, addressed as captain) submarines, destroyers, etc. at ranks from LT to LCDR.
The Enterprise is the fleet flagship, sure, and no doubt many other senior officers will resent being passed over by a freshly minted lieutenant, but Kirk just saved the world, its a great propaganda move, and why change a crew dynamic that clearly works very well?
The system-system beaming potential is more troubling to me, but it will no doubt be technobabbled away as a one-shot, overly dangerous plot device.