I agree with this as a loss of control of healing output. I can see both Holy and Disc wanting predictable/unchanging HoT speeds. Holy can use HoTs to top people off, or throw HoTs to control damage while a bigger heal is spooling up. Disc can toss them as a nice fire & forget on group members during AoE damage while they concentrate on the tank. Haste being an unavoidable element of caster gear that speeds up HoTs will mean you'll have to do more and more direct healing as you gear up... essentially pushing Holy toward Disc gameplay and making Disc more frantic.

I can also see Shadow having trouble with this too. Sure it will might increase dps and dpm, however Shadow's rotation is already an act in balancing on a razor's edge. This will change your spell expire time as you gear up, and may at some point create dead zones in your rotation/priority list easily. If you are waiting for a spell to come off of CD and it had less than a GCD to go, but one of your DoTs expires before then, you're in a bad spot. You need to keep your DoTs rolling, however if you push that DoT you're adding a GCD to your long spell's CD, decreasing DPS. It may be that given your current haste rating and DoT speedup due to haste, there is no better cast sequence. One of the biggest problems with this is not only that this balance could change heavily as you gear up, but that buffs, elixirs, procs, and fight mechanics can rebalance all of this in an instant... and it is possible that your CD sequence before a given haste proc or buff may tank your DPS once you have the buff since your entirely priority system has changed, and it may make reshuffling your CDs once the haste buff/proc has very difficult.

I'm not sure this is a good idea for any spec of Priest.