I know size of the ship is still being fiercely debated but at 725 meters from the official source. That makes it larger than the Enterprise-E from TNG.
No it doesn't. It makes it LONGER than the Enterprise-E while having similar internal volume (and less than 70% the volume of the Enterprise-D). Size wise it's actually closer to the Ambassador class, just with larger nacelles.
With a ship that size, what was Kirk thinking putting it in a situation where it can be exposed like that. It's not like the transporters or shuttlecrafts weren't operable.
It's EXACTLY like the transporters and shuttlecraft weren't operable. The whole point of having to physically land the ship was that the magnetic field around the volcano was screwing up their transporters and they couldn't use the transporters except at incredibly close range. As we saw with Kirk and McCoy's narrow escape, having your ship parked literally within walking distance of the landing site does have certain advantages.
You should really stop using Ex-astris-scientia as a trek source. The author of that site is a bit of a neurotic.