No, it would require much more work than you think.
There are a lot of fights that rely heavily on one-shots or ring-outs. You can't heal through those. So existing and future fights would need to be redesigned to reduce reliance on these things.
All damage is scripted, and healers not needing to worry about random incoming damage is a big reason why we're able to spend most of our time DPSing. So you'd need to redesign all future and existing fights to include some randomly-targeted unavoidable attacks.
It's not as simple as just cranking a knob and making numbers go up. Our healing kits are almost as boring as our DPS kits, because they consist almost exclusively of oGCD cooldowns. Cranking boss auto-attacks up only means that now we're spamming Cure 2/Adlo/Benefic 2 instead of Glare/Broil/Malefic. Not only would most healing oGCDs need to be nuked from orbit, you'd also need to add more GCD healing tools, and probably overhaul how MP works in the process, to make GCD-heavy healing engaging. Besides which, there are too many situations in this game where healing just doesn't matter, usually because a failed mechanic will wipe the party anyway.
As others have stated, FF14 has designed itself into a corner with a reliance on burst healing. Breaking out of that corner means completely overhauling the role to match the sustain healing that you see in other MMOs. It would be far easier for Square to just make healer DPS more engaging or give healers some active support to do (though the latter is less likely, because support keeps going to Ranged DPS instead).
And as I keep saying, there is precedent with tanks. Most other MMOs focus on sustained threat management and sustained active mitigation. FF14's threat management is a button you push to turn on tank stance, and mitigation is all oGCD cooldowns, because tankbusters are the only things that need to be mitigated, and they're on a script. In 5.0, Square bit the bullet and turned tanks into Blue DPS, recognizing that the community was already playing them that way anyway.
At least with butts, one can claim that the forums were melting down over the issue.
I'd be more worried why Yoshida felt that revamping FSH, of all things, was more critical than fixing healers.