Yes, in the original series, it was clearly impossible to beam anywhere or from anywhere without having a transporter pad at one end of the process at least.
In the spinoffs since TNG, this has not been impossible. And saving power has never really been a concern for our heroes, because they always have plenty to spare - the transporter is a very low-power application compared with other Trek staples such as warp drives or shields, apparently. See for example ST4:The Voyage Home, where the Klingon ship is basically powerless but can effortlessly run a cloaking device and has very little trouble performing these "site-to-site" transports, even for completely frivolous purposes (Jim is beamed aboard, allowing Gillian to jump in, even though all the other heroes just walked in through the door!).
However, even if the pads themselves are completely unnecessary in the 24th century, the room still serves a purpose. It's a staging area (because away teams need equipment, and this should be stored in a centralized manner instead of keeping one of everything in every room), and it's a boarding room and quarantine gateway as well. If the room did not exist, most items and people should be beamed site-to-site to dedicated quarantine facilities or holding cells anyway.
What is unrealistic about the setup is the failure to use site-to-site more often, in situations where quarantine or gearing up is not a requirement. That's done for the drama - there are certain types of dialogue that require
waiting before transport, a concept that shouldn't exist if site-to-site transport were available. But we can always argue Starfleet is conservative (or even paranoid) about certain safety measures and therefore only allows site-to-site in emergencies.
Also, the transporter "antennas" might point outwards and using them for intership beaming is using the system in a way it wasn't really intended.
Makes a lot of sense. Although we have seen the transporter move items from outside the ship to inside the ship with absolute precision, this could be because the antennas point outward but the signal then travels along wires to the transporter pad; aiming it anywhere else would require beams rather than wires, and those might have real trouble focusing inward or close up.
Timo Saloniemi