The quadratic pricing comes from the enchantment rules. Powerstones are made by taking a gem, making it into a 1-point stone, making that into a 2-point, and so on. But there's a chance of failure on each operation, which gives the 'stone a quirk, and critical failure will destroy it. There's an example on p. 17 of GURPS Magic, while the full enchantment description is on pp. 69-70.
The 6-foot recharge rule means that you have to let powerstones out of your immediate control to get them to recharge as quickly as possible. That makes larger 'stones more attractive, simply because it's easier to keep track of them. This applies both to their energy content (fewer things to track) and their location, especially if other members of your party, carrying your stones to separate them for charging, get bored and start swapping them around. Been there, done that.
Since spellcasting energy is the primary resource-tracking that GURPS magicians have to do, some players are happy to cope with complexity if it gets you more total power for less money, while other prefer to keep things simple.
"Quirks" are individual peculiarities of powerstones, named by analogy with the quirks (1-point disadvantages) of GURPS characters. Most of them are restrictions on the stone's recharging or its usage. A badly quirked stone might only recharge while immersed in flowing water, but only be usable for casting fire college spells at night-time. The GM creates stones' quirks in any way they find appropriate.
Adventurers generally prefer Powerstones without quirks, and usually have the money to pay for them. Magicians who don't adventure can have physical security for keeping their 'stones safe while recharging, and can more easily cope with quirked stones, because their working environment is more predictable.
Having an aspect of the game be an emergent property of the (fairly simple) enchantment rules, rather than changing the rules to produce a specific style of gameplay is an example of the difference in philosophy between GURPS and modern editions of D&D. It did happen that way round: the calculations for Powerstone costs were done for an article in Roleplayer magazine, some time after the enchantment rules were first published.
I left out expensive spells because the OP was discounting them, but @Zeiss Ikon's answer shows how you can suddenly find yourself needing an extra 10 or 20 energy, and a medium-large powerstone is a life-saver under those circumstances.