Suppressive fire is already an obselete doctrine. That's why the British army is replacing their machine guns with DMRs (Canadian military may be heading in the same direction).
Turns out turning a motherfuckers head into a fine red mist with a 7.62 tends to make everyone else around them really eager to seek cover. The threat of a well placed shot has a far better suppressing effect than the reality of a bunch of inaccurate fire.
I'd imagine a sniper is probably one of the most effective ways to suppress a group. They probably don't know where the shots are coming from, and don't know when it's safe to move again.
Having said that, I would imagine there are situations where traditional suppression is better. A hail of bullets against the side of an APC is probably terrifying even if none of them are getting through. It's going to be tough to get someone to open the hatch as the bullets are flying in. But, with designated marksmen only, you'd have to wait until the enemy tries to get out of the APC and then make a tough shot to hit them as they do.
So, basically what the USSR did ? (IIRC, machine gunners and sharpshooters carrying some semi auto scoped rifle were basically interchangeable in their doctrine, at least during WW2)