The problem with the size of Starfleet is that it roughly equivalent to the other major Alpha quadrant powers. UFP herself is responsible, if the Starfleet were to have the same ship per sector ratio as other powers it would have ?4-5 as many ships as the other powers. A military buildup of that size would provoke the other powers and could lead to war.
Another thing is that from my point of view all the powers are using pre-WWI military policy. Only/mostly using professional armies, that means there is no draft, the standard of living doesn't change until you are conquered ...
On the Cloaking device:
It is an advantage to have one, but it also brings disadvantages. I think that when at Warp under Cloak, the faster the speed the higher the emissions the higher is the chance the ship is detected. On the other hand the lower the speed the longer it takes to get somewhere and you can get detected. Also if a lot ships travel under cloak - of course someone would investigate all those anomalies.
This ought to be possible only if you know how a Cloaking device works - which UFP does, they obtained one and even built one superior to the Romulan one - and have good sensors.
This explains why the Klingons were able to conquer Cardassia - Bajor and Cardassia are neighbors and the Cardassians don't have as good sensors as UFP.
Klingons conquering Romulans could be explained in a similar way, after all no one Romulus detected a cloaked Klingon bird-of-prey.
Also imagine if during a battle more ships were to use the Cloaking device, the chance that two friendly cloaked ships were to collide would increase and what about a cloaked fleet travelling, a small drift and the formation is lost.