When you start decking yourself out in all purple and gold, primary weapons and machine guns turn into laser beams. The only ones worth using are so easy to control that you rarely miss a shot. SUROS' strength comes not from it's worst-in-class DPS on the top half of its magazine, but the fact that there is like zero kick so every shot is on target. You always get maximum DPS with practically no effort.
Every heavy machine gun is going to be made several times more effective with a weapon stability perk. It increases their effective optimal kill range to ridiculous lengths that provide little counter play, and removes all sense of power in the gun.
The kick makes a gun [u]feel[/u] way more fun and is much more engaging to use. But the ridiculous sponginess of the enemies all but demands we have 100% damage uptime when out of cover or we're not going to have fun. So we have to sacrifice the short term joy of using a heavy weapon to mitigate the long term frustration of whittling down an enemy.
In Crucible, simply reducing the effectiveness of fitted stock and rodeo is sufficient (you could also make an argument to put Auto Rifle damage back to the way it was) because the guns still kill extremely quickly.
In PvE we're going to have an entirely different set of problems from messing with the core gameplay loop but at least the guns will be fun.
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So, what exactly are you trying to say? You suggest that endgame weapons with high stability should have that mitigated to make them more fun and rewarding to handle? That's great and all, but you pretty much explained why this won't ever happen. The enemies are hardcore bullet sponges. We NEED that stability so we can keep all our guns trained on their weak spots. If we were to have the stability/recoil of all the worthwhile endgame weapons reduced as a whole, then a good number of enemies would need to have their health/damage resistance adjusted to compromise. I can say for sure, right now, that with all the problems on their plate, Bungie wouldn't even go through the trouble.