The flaw isn't in the concept but in the execution, or more specifically in the writing. And the post-production limitations.
In "The Cage" we saw the landing party beam down with field jackets and equipment in backpacks. For an extended survey task that makes sense and should have been seen throughout TOS. The introduction of the tricorder in TOS could rationalize why more and bulkier equipment (as seen in "The Cage") was largely no longer needed. The field jackets or some updated version of them would have been nice to see again. The idea was brought back in TMP, TWOK and TFF. We could assume there were TOS style field jackets but we just never had occasion to see them. The planet in "Spock's Brain" would have been the ideal place to see them again, but they just didn't have the budget to supply them. You could apply similar reasoning to the female uniform which was fine for aboard ship, but really had no business on a landing party assignment. Here the woman should have had an alternate uniform (pants) for landing party duty.
If we assume the transporter of the Pike/Kirk era is largely safe and effective then it is a faster and more convenient method of getting personnel off and on ship. The shuttlecraft is a more involved and time consuming mode of transport suitable to only certain conditions: the ship has to be somewhere else, use of the transporter is inadvisable or the shuttlecraft can go where the starship can't. Those conditions hinge on how events in a story are set up. In "The Galileo Seven" wouldn't have been safer to send the Enterprise
into the Murasaki effect as opposed to a shuttlecraft? The ship had to go in there anyway afterward to search for the shuttlecraft and it's systems didn't go haywire. Or maybe they just didn't anticipate the shuttlecraft having any difficulty.