Without any levelling based on "experience", Eve's skills become the only method for controlling who can do what in the game; what ships, what modules, what charges and how well they work.
Some skills are prerequisites for using items or flying ships, or sometimes they are prerequisites for other skills and have little or no value on their own. Other skills are not required but have enhancement values that improve how well your character can use something.
Technically, no skill is "needed". You character is free to spend years untrained as a one day old newbie. But that is unrealistic. At a minimum you want access to some fancier ships capable of whatever you have your heart set on, and most players want access to many types of ships for different roles.
If you want to fly an interceptor, you need Caldari Frigate V and Interceptors I. If you want to fly an interceptor well, you want a lot more skills.
Unless I want to fly a Marauder Battleship, you don't need to train Advanced Weapon Upgrades to level V and considering its a 27+ day skill, its understandable why a pilot might avoid it. After all, it only reduces weapon turrets and launchers powergrid needs by 2%. so you might want to train it, but its not a need.
However, sometimes want can turn into need.
A lot of ship fittings I'm looking at could really benefit from that skill. When you have 8 Blaster Cannons on your Rokh using 2174 MW each, an additional 2% savings is over 376 MW, enough to power two tech 2 Large Shield Extenders. For cruiser sized ships its not as extreme but it is still considerable. It is often the difference between highest damage weapons and medium damage weapons, or having a decent tank or just an OK one.
Yeah, that want has turned into need. Alas, I've added it to the list of summer training. Sigh.
On the upside, it will allow me to fly a Golem Marauder when complete.