[JamOfBoy]

High Speed Divine Words right now has very limited value. HSDW only starts paying itself back in terms of momentum after the first invocation, and typically you'd sooner just Charge Mind to get the most out of one cast. Being able to splice in actions before beginning the invocation is useful, sure, and it'd undoubtedly be useful on classes that AREN'T Evoker (evoker has next-to-nothing to do with 4m prior to casting except moving). That being said, I don't think HSDW should be given to everyone. Evoker undoubtedly needs changing, HSDW undoubtedly needs changing, but this doesn't seem like the way to go for me. High Speed Divine Words is part of Evoker's identity, and it should remain part of Evoker's identity, otherwise you'd be giving a mediocre class even less reason to be picked.

Divine shower with hsdw... That would be totally broken in any kind of scenario.

No, I think it'd be fine. Evoker/Priests are scary because of the modifiers to spells Evoker innates and passives grant Priest's mapwide multi-hit invoke, and even then it simply makes them do as much damage as all of Evoker's invocations anyway - they're the same scaling, 180% ele, 100% SWA. HSDW is as potent as it is for Priest as it is for Evoker, no more no less.