build ships that are simpler to use, focus on more advanced tactics. Also, if I remember correctly, Kor had Kirk badly outnumbered.
Outnumbered yes with garrison troops equipped to pacify people with medieval technology. He also was unaware of there being Federation officers on the planet. Kirks disguise and actions make him both a spy and a terrorist. Kor with Garrison troops not knowing who or what he faced beat Kirk while maintaining his control of the planet. Kirk at least knew who and what he was fighting and still lost.
F-CA is built for long term survey cruises. It has more labs, and its engines are designed for operating for extended periods of time at relatively high speeds. It also requires greater habitability. Hence the greater size that you keep harping on. The D7 could avoid adding new mounts because increasing its fire power was merely a matter of upgrading some of the inferior phaser mountings that it was built with.
Compare the F-CA to the actual F-GCS survey cruiser.
You will notice the CA is deficient in several areas:
special sensors
transporters
shuttles
drones for probes
defensive weapons.
The actual survey ship on the other hand though it can function as a CVL is lacking in offensive firepower.
Now consider the Klingon survey ship. Like the F-GCS it has special sensors. It doesn't gain transporters, or drones because the Klingon ships are better equipped that way to start. It does however take a big hit in offensive firepower being traded for defensive. The same applies to the Romulan Survey ship.
Now answer the question why would the Federation keep making CA class ships during the Galactic War instead of making actual specialized warships? The Vulcans would surely explain the illogic in not making specialized CAs. Why also does this supposed exploration ship lack the common components of those explicitly exploration ships while having the full
OFFENSIVE armaments of the CA it is named as?
Is the Federation "We come in peace" real or is it a lie? This as you call it survey ship is far heavier armed than the Klingon survey ship which of us is the eonquerer?
As to the high speed long range ability with few exceptions (Tholian and Wyn) all the CAs should have that ability = deep strikes are only possible if you have them. Just consider how far Klingon ships sold to the Romulans had to travel to get to Romulus for refitting to Romulan weapons and control systems. Not possible without that high speed and long range ability and those were versions we were willing to sell.
The F-CA needs the greater habitability because the crew is soft, it is not warrior trained and is unable to endure without luxury. The Klingon ship and crew constitute a lean mean fighting machine. The Federation ships reflect their crews - fat and lazy.
Klingons go into battle drunk, more often than not, and still come out on top.
I for one don't drink.
I do insist on the same rules for drinking of the old French Foreign Legion. Namely there are none. However there are harch punishments for rendering yourself unfit for duty.