I have seen nearly every episode (other than enterprise and some ds9), and except in very rare cases (such as the borg) there has never been any kind of personal protection, either personal shields or even body armor. Given the number of wounds and deaths we see in any kind of ground battle, it seems strange that everyone runs around in flimsy cloth uniforms. Why has this never been an issue?"
I think it's a Federation policy that in first contact or diplomatic missions you'll approach the other side on the same "footing".
If Starfleet personnel would conduct such encounters with some kind of body armor it would immediately cause skepticism and suspicions ("if you say you come in peace why are you wearing body armor?!?"). Looks like the phaser type 1 for self defense is the only thing other humanoid species will consider acceptable.
And it ensures that every
Starfleet vessel commander will
do a proper amount of research of an alien culture before beaming personnel down to another planet.
Might be a totally different thing with the Klingon Empire but if I recall from TOS "Friday's Child" correctly, the Klingon uniform, then, is not projectile-proof, either.
The American Football uniforms seen in ST I, III and IV are of course a completely different matter as they serve only UFP internal security purposes.