Yeah, I'm seeing a lot of people not getting the issue. So I'm gonna storytime it.
Dusty the Destroyer, our 15th level deluded hero, has decided to learn Destruction. He seeks out a trainer, and gets his 5 trainings for the level, which continues to limit him to baby spells. He heads to a dungeon to gather loot so he can pay for more training. He picks a long one with plentiful enemies, most of them melee. Due to this, he gains multiple skillups in his armor, weapon, block, and even a bit of alchemy (after a short stop at a alchemy table to make some more poisons out of all that bone meal). He's ready to level, but only made about 600 septims profit. That's not enough for 5 training sessions, so he declines to level, and finds another dungeon. He gets more skillups during this, and finally gets enough to pay for his trainings. He even lucks out and gets a few choice items that he enchants to raise their price, gaining a couple more skillups. So he trains 5 times, and then levels.
OH NO! Dusty gained 2 levels when he only wanted 1, and then was going to train again before taking that second level! That opportunity to train is completely lost to him now, there's no way to get it back!
Dusty is thankful, however, that he wasn't training his 1h skill, because that would have taken him 10+ levels to get enough money together to pay for the training. Maybe he'll join the Thieves Guild, even though he hates them with a passion...just so he can make enough money to pay those price-gouging trainers!
Dusty should actually use Destruction then. Most dungeons and places are filled with very easy target practice and one single hard boss at the end. Dusty can level up destruction on the target practice and take out the boss with melee. This is even more beneficial than training if you look at it this way.
Level 15: 20 Destruction - 50 One Handed - 50 Light Armor
Destruction used 70% of the time in combat and 10% is melee against those hard bosses and 20% is armor skill-ups.
Level 16: 27 Destruction - 51 One Handed - 52 Light Armor
Level 17: 34 Destruction - 52 One Handed - 54 Light Armor
Level 18: 41 Destruction - 53 One Handed - 56 Light Armor
Level 19: 48 Destruction - 54 One Handed - 58 Light Armor
Level 20: 55 Destruction - 55 One Handed - 60 Light Armor
In 5 levels he became quite the magister and he used his weapon skills relatively little in comparison.
Destruction used 0% of the time but 5 skill ups a level, 60% is melee and 40% is armor skill-ups (more since he is in melee now).
Level 16: 25 Destruction - 56 One Handed - 54 Light Armor
Level 17: 30 Destruction - 62 One Handed - 58 Light Armor
Level 18: 35 Destruction - 68 One Handed - 62 Light Armor
Level 19: 40 Destruction - 74 One Handed - 66 Light Armor
Level 20: 45 Destruction - 80 One Handed - 70 Light Armor
Dusty is still even more melee centric and not too much of a mage in comparison.
If Dusty truly liked the Destruction spell school he would not mind leveling using destruction. The way I see it Dusty's true passion is actually melee.