One of my current characters is a Bosmer archer that also relies on illusion spells.

Correct me if I'm wrong, but your amount of magicka depends on your intelligence stat, which governs alchemy, conjuration and mysticism.

So if I don't use any of those skills, my overall MP won't increase?

Magicka pool = 2 x Intelligence + any bonuses (racial, birthsign)

If you never raise your Intelligence when leveling up, then your Magicka pool will not increase. You can use enchanted items with Fortify Magicka and/or Fortify Intelligence to increase it otherwise.

You could still raise intelligence 1 point per level. You could also pay for training in one of those skills to raise it by more.

That's... pretty stupid.

I shouldn't be forced to use certain skills so I will be able to do what I actually want.

In other words, effective practice of any of the schools of magic depends on whether you level up mysticism, alchemy or conjuration.

A couple of transcendent sigil stones will solve your problem.

Not completely. As your skill in any school of magic increases, the cost of casting the spell goes down. So as you improve Illusion, your available Magicka pool will go further.

But if you want to cast big spells, then yes, you have to level up those three.

I have a Mage character I'm playing and I have to level up Heavy Armor (which he doesn't wear), Armorer (which he doesn't need to use often) and Block (also rarely used) just to increase Health.

That's how the game works.

Though to be honest, Intelligence is astoundingly easy to level. Sit there with a mortar and pestle and churn out restore fatigue potions made from food items, and sell them to vendors. You don't have to use the potions for anything if that violates some roleplaying rule you have imposed on yourself.

Conjuration skyrockets up. I think it is the fastest magic school to level by far. Learn a custom 1-sec duration Bound Dagger and cast it over and over. At low levels it will increase literally with every cast.

This flawed game mechanic still is at fault here. I shouldn't actually need to resort to alternative measures.

But out of the options laid out for me, doing/starting the MQ is preferable.

Grant soul gems will also give you 24 magicka, so you can do that instead of the main quest, provided you have access to an enchanting station and can cast the fortify magic effect. But a transcendent sigil stone with the fortify magic effect on it will give you 50 magicka without having to worry about any of that.

Sounds good to me. If you enchant every piece in your gear that should be enough for a pretty large magicka pool.

Three pieces of gear with Transcendent Sigil Stones would be more of a Magicka increase (+150) than maxing your Intelligence at 100 from a starting value of 30 (+140). If you wear armor, rings, necklace, and carry a shield you would have 9 possible enchantment slots. So you'd still have 6 for other useful enchantments.

Though note that if you don't increase those magic schools, you won't have as many spell effects available for custom enchanting either. So you'd need to rely on Sigil Stones only, Novice level spell effects, or get the spell effects from doomstones.

Yeah, there are several doomstone a that will give you fortify magicka. Or any of the magical races or birthsigns. I think you need 50 restoration to cast the spell, but it might only be 25. Can't recall. But 9 pieces of gear enchanted with grand soul gems will give you 226 magicka, which is plenty.

"I shouldn't be forced to use certain skills so I will be able to do what I actually want."

Most RPG games before Morrowind you leveled up according to how many monsters you killed regardless how you killed them. You see a group of ogres coming toward you and call in an artillery strike, you killed the monsters and go up a level. Then you get to pick increase in blade, sneak, pickpocketing, whatever even though you never actually practiced any of those skills. Bethesda felt, and I agree, that a level up system based on skill usage rather than monster kill statistics was more realistic.

Three ways to deal with it;
1. Try another RPG game, most of them level up via a kill points system and you can add all your bonus points to musical talent, hairstyling, and political correctness even if you never actually used anything that would increase those.
2. Buy the bound dagger spell in the Chorrol mages guild, cast it over and over until it hits 25. Then but the basic skeleton from the same guy, every time you summon him your conjuration increases and you can also practice on him to increase destruction spells, weapon skills, and armor skills when he fights back. Just let him hit you and the armor skill increases, then heal yourself to increase restoration, repair the damage to increase armor repair. An hour or so casting spells at a summoned skeleton you get intelligence, will, strength, endurance, speed, agility, only bonus points you can't get fighting your skeleton is luck and personality.

3. If you really hate it, cheat. Open the construction set and make yourself a mod. Gameplay, Game Settings, iLevelUp01Mult through iLevelUp10Mult, change them all to 5 or 10 or however much you want to cheat.

This is one thing Skyrim did right. You master a skill by using it and then leveling up. No illogical requirements.

I like Oblivion's system just fine.

While I agree the system in Oblivion is not perfect. I think it is million times better than a system where you can have ton of magicka when you don't actually practice any magic at all. Yes you don't need to plan much with your characters when playing Skyrim, and that's exactly where the fun was taken away IMO.

The problem in this particular one is that while knowing a lot of Illusion should make one more appealing thus have higher "personality", I do not see how being a more charming person gives one advantage in casting illusion magic. The governing attribute for illusion should actually be intelligence to be logical. At least that's how I think about it.

But you should not worry about not having enough magicka if all you are ever going to use is illusion magic, a lot of the useful illusion spells like invisibility or charm are quite cheap to cast as I recall. And you can always just stick to the lower level spells for paralysis since they are very powerful to begin with.

Years ago a modder named Kobu invented a revolutionary system to handle Attributes that I hope Bethesda adopts if they ever bring Attributes back. He called it The Great Wheel. The Great Wheel arranges the seven Attributes into a circle. Each Attribute is given two primary associations, two secondary associations and two with no associations. In the case of Illusion, 70% would go to Personality, 15% to Intelligence, 10% to Willpower and 5% to Agility.

I believe a system like this would help to reduce frustrations like yours. It was such a fantastic idea that several well-known mods (such as nGCD and Realistic Leveling) borrowed it.