No it won't, it'll reinforce the idea that is a force of destruction that can be used at the whims of people born richer than you. And mages, of course, will continue to be (justifiably) resented.
How so? That isn't going to be laid upon them unless if they happen to be breaking the law, Obviously there could be collateral damage and all, such as if Bandits were operating in a city, but in that case, there would be no reason to even employ their services, My point was merely that could be used in situations where standard forces would not be enough.
Such in the case of Monsters, Bandits and etc.
And resentment will follow magic wherever it goes, at least this way they will be paid well for the services that are beneficial to the community.
Healing reserved for "higher-tiered citizenry"? That is back-asswards.
Healers are among the rarest of Mages, That school is rarely taught, even rarer is you find someone good in it, So Yes until it got more common place it should remain as is, Heads of State and others that can actually foot the bill for that luxury.
That is literally what you said, though, that beyond whatever uses the state (or the crown) would have for the mages, any faction and individual wealthy enough could also utilize these services. So our logic here is:
It really isn't.
As i said before, the Chantry and State would constitute what could be legally done with those services, and i doubt either would approve of mass murder of the peasantry. For fairly obvious reasons.
"Mages need to be isolated and locked up for your safety! They could go crazy and kill you and your family at any moment! Now, if some blue blood pays a mage to atomize you, that's fine."
If Blue Bloods want to pay to atomize the people that harass, kill and rob you is more accurate.
After all, if a supply caravan is robbed, not only are the peasantry going to suffer from the lack of supplies, the actual owners of the merchant caravan are going to lose money, its a system that will help both parties.