While a 'handful' of karma may not seem like a lot, it certainly costs more than the potential drain paid by someone breaking it.
Now have those quickened spells broken a few times and you will find replacing them over and over can get spendy.
And if you think someone is NOT going to try breaking said spells, especially if it is making you more effective, you are mistaken.
I agree with all your points except this one. Assuming a Human Mage with 7 Edge (because he wants to survive the drain), let's look at some numbers.
Increase Reflexes - Drain = F
Force 12 = 12S or P Drain. Spellcasting 6 + Health Specialization 2 + Mentor Spirit 2 + Magic 6 + Force 6 Bound Spirit (Aid Sorcery) + Health Spellcasting Focus 4 = 26 dice to cast. Averaging about 9 hits. Using Edge to reroll, that's another 6 hits. Capping at the limit of 12, you now have a whopping +12, +4d6 (total of 5d6) to your Initiative. For forever.
Now, what about Drain? Assuming a Drain stat of 6 and a Willpower of 5, that's 11 dice to resist 12P Drain. Using Edge 7 to Push the Limit, you are going to get 6-7 hits on average. That's a mere 5P Drain. Easy enough to soak.
Your argument, then, is that it will be dispelled. Actually, since it's a Force 12 spell, this Human Mage decides to spend 12 Karma to quicken it.
The test to dispel it then becomes Counterspelling + Magic [Astral] vs. Spell's Force (12) + Caster's Magic (6) + Amount of Karma spent to quicken (12). Or, in other words, Counterspelling + Magic [Astral] vs. 30 dice. Assuming those dice roll completely average, that's 10 hits. A Magic 6, Counterspelling 6 Mage is only rolling 12 dice. And that's not the end of it. They are limited by their Astral Limit. A Charisma 9, Willpower 6, Essence 6 Mage only has a Social (and thus Astral) limit of 10. And you won't find that anywhere, really. If we were to take a Magic 10, Counterspelling 13 mage, they still only roll 23 dice. That requires at least 4 Initiations, and 366 Karma (126 to raise Counterspelling from 7 to 13; 70 from 4 Initiations; and 170 to raise Magic from 6 to 10). That's 366 Karma vs 25 Karma from the casting Mage. And no guarantee for the 366 Karma Mage to succeed. In fact, unless they spend Edge, it's nearly impossible to even touch the spell.
To top it all off, whether or not you were successful at counterspelling it, you have to resist 12P Drain. Fun, fun, fun. You don't even get rid of the spell until 12 net hits.
Basically, no. If someone is willing to invest the, quite appropriate, amount of resources into a massive spell, they can quicken it without ever worrying about it being dispelled.
Basically, yes, if used correctly, Quickening is broken as hell. That's why people houserule it all the time, in order to bring it's power down a bit. Hell, Harlequinn, while badass in his own right, is mostly what he is by the fact that he has a billion buffs quickened on himself (and his access to all spells, etc; that's besides the point).