Putting Assize on a longer CD would further hamper WHM's MP economy.
Also, WHM needs more oGCDs, not less, so merging Assize and PI just takes away from WHM's toolkit as a whole instead of expanding on them.
Finally, this version of Assize/PI would be a nerf because you would have to wait a minimum of 10 seconds just to match Assize's current Healing potency while also removing the AoE buffer that PI currently is, just for a 200 potency gain after 20 seconds.

I understand the desire to make Assize more useful as a Healing tool, however, this is not how you do it. Personally, I honestly don't think there is a good way to make current Assize into a Healing Tool because it has MP restore attached to it and that alone makes it much more important than the actual heal, while the damage component just compounds that issue even further. That isn't to say it can't be made into a useful tool for WHM but I don't think making it heal is the way to go about it. If it offered a Shield effect or reduced the damage enemies did, it would still be a useful tool for WHM to utilize but there are times when the heal on Assize is actually useful so even that idea isn't without its flaws.. The buff suggestion could work also, so that you could manually trigger the heal as needed but building stacks in order for it to heal just as much as it currently does isn't the greatest suggestions cause there will be instances when you need the heal immediately and you'd get less out of it as a result. It would need to heal for a flat amount that is equal to, or more than, what Assize currently heals for while the buff is active for it to see usage as a healing tool but since the MP restore and Damage components are still there, it's not guaranteed that you'll need the heal during that time either so even that idea, while probably the best compromise, has its limits too.

Either the Damage/MP restore on Assize need to be placed on an alternative skill or the healing component needs to be changed because Assize just has too much going on with it to be effective as a healing skill.