It would create quite a few problems, rather than balance.

Nominally, it is easier to stack Weapon Damage than it is to stack Spell Damage, which would result in Stamina builds having more overall power potential than Magicka builds. In fact, this is the current point of contention with the scaling for procs on the PTS, as the changes will likely end up with Stamina builds gaining more damage in PVP from procs than the Magicka builds who previously relied on procs to bring their damage in PVP up to Stamina levels. Keeping it so that skills, damage and healing, to scale from both W/S Damage and Stamina/Magicka helps alleviate that discrepancy.

From a PVE perspective, DDs having decent healing or defense potential, or healers having decent damage potential, or even tanks having decent damage potential isn't that much of a problem. So, I'll focus a bit more on PVP.

Also, the way I see it, there are two types of defense. Passive defense obtained through methods such as Max Health, Health Regen, Armor/Resistances, and Damage Mitigation. And, Reactive defense obtained through Heals, Shields, Positioning, Dodging, and Mobility. Passive defense is about being able to take a hit, while active defense is about being able to respond to a hit. Builds being able to do damage while having reactive defense is, IMO, not as much a problem as builds being able to do damage while having passive defense.

For example... A 20K Health build being able to heal back from a 15K burst is still a build that could die after a 15K burst—it just depends on who reacts to the burst better in combat. On the other hand, a 40K Health build being able to heal back from a 15K burst is a build who will very rarely die after that 15K burst. Allowing the 20K Health build to do better damage than the 40K Health build makes that 20K Health build more enticing—people like being able to kill stuff. However, people also tend to not like dying, and so will gravitate towards ways to avoid doing so. If people can't survive on the 20K build at all, they won't go with that option, and will gravitate towards the 40K build. Even more so if the 40K build can do damage close to (or better than) the 20K build. This is how we end up with tank or proc metas—people find builds that can be effective at passive defense and damage. So, in order to encourage more people to run builds that result in an overall lower TTK—and therefore more fun/dynamic PVP—there has to be the ability for reactive defense to satisfy their desire to not die couple with the access to damage to satisfy the desire to kill. (I hope this is making sense.)

The other way to look at is that healing and shields are the "Magickal" defensive options. Taking away the effectiveness of Magicka DDs in PVP to access reliable defensive options puts them at a further disadvantage compared to Stamina DDs who rely more so on mobility and dodge-rolling for defense.

There are, perhaps, better ways to cut down on healing potential without eliminating any sort of efficacy. One such way would be to reduce the strength of heals across the board by a bit, but then buff sources of % Healing Done / % Healing Received by more. In essence, make not using those sources a bit less effective (5% less perhaps), while also making using those sources greatly more enticing (10% more perhaps). The overall problem is that ZOS recently has opted more so for negative punishment in discouraging builds (and often with adverse effects), rather than opting for positive reinforcement.