One thing i have notice often if not always, when Federation are exploring unknown sector that could be potential dangerous. It seems Star-fleet always sends only one ship. Why don't they send a couple of ships(a least 2-3 ships) together, when they decide explore unknown sector. Safety in numbers makes more sense doesn't it. If look back during the Age of Discovery when European navigators traveled around the world discovering new lands and cultures. We can see that famous explorer f.e. Christopher Columbus, Vasco da Gama, Ferdinand Magellan, Hernán Cortés, Jacques Cartier, James Cook and many more usually had more then one ship when they began their voyages.
Well the question you ask when allocating resources is not "why send less?" but "why send more?". If Starfleet has a single ship capable of doing the job (as they clearly do) then why send two or three? Safety in numbers is all well and good but it doesn't help if you get swatted by something new and dangerous, you just lose X ships instead of 1. Going into something new you limit your risk by sending one ship, as you pointed out yourself the ancient explorers generally STARTED with multiple ships, they often did not have that many when they got home.
One reason is budgetary. If Enterprise can do everything from fight to conduct delicate scientific research why send Enterprise and Yamato. Secondly space travel is much safer then travel during the age of sail. If ships are not lost due to a high rate of accidents you don't send backups that are not needed. Third a fleet turning towards you is more provocative then a single ship. It is said that Lewis and Clarke were able to avoid many fights because a woman was with them. Being a solo ship makes a similar statement. But the most important reason. If Kirk was not alone then Kirk does not look as heroic to the TV audience
The only REAL reason is to hype the drama. It's more exciting if there is no help around and if our heroes fail the universe will be turned into a giant glazed donut or whatever...
Anything more than 1 ship does not look diplomatic or scientific, it looks like an invasion. Of course send 1 ship, makes sense diplomatically.
As of TNG-era Trek, and to some degree TOS and well, we might note that Starfleet doesn't really "send" ships. When there are emergencies, the hero ship simply drops whatever Starfleet has sent her to do and sprints to the rescue. Starfleet couldn't really organize a fleet of six starships to respond to the crisis du jour, because the crisis would be past by then. When we see the Enterprise on the spot, she's not the only starship there - she is the first one. While others might follow in a day or two, the first ship on the scene usually makes an assessment that stops those other ships from abusing their warp drives. Either it is something the Enterprise can easily handle, or then something so serious that flying in additional ships piecemeal would not help any. Timo Saloniemi
I'm pretty sure they only send 1 ship to a certain area... but there is usually the rest of the "fleet" near by