The PTRD and PTRS the Soviets used in WW2 were roughly .55 cal (14.1mm or so I think) that could penetrate 40mm of face hardened steel at 100m. And they were like 5 feet long, too.
A 20mm version was produced but I couldn't find a lot of info other than it wasn't used much since by that time towards the end of the war the RPG's (not to mention bazookas showing up)were getting better and becoming the standard AT weapon. Which was why the Germans started putting skirts and spaced armor on their tanks.
Still, the PTRD was good enough that the Russians used them in huge numbers - even against Tigers they could at make a soft kill by breaking a track.
So this was probably what was discussed before.
The Barrett only weighs 36 pounds, so its not inconceivable that it could be hauled around as a weapon that might be used as a combat rifle - and the sniper teams have only two guys that operate alone with one of them carrying a regular assault weapon to help protect the sniper, but the sniper has to carry the big gun.
Given its size and the close quarters involved I imagine a tactical transition by sniper from his Barrett to a pistol or whatever would be kind awkward. If you had it loaded and ready in your hands, came around the corner and found a bad guy in front you it'd be easier and instinctive to just vaporize him with the big gun. I've smacked guys with flashlights because it was already in my hand, and while my ASP would have been a better choice (its awfully hard on the flashlight and doesn't have as much reach or authoritative effect as an ASP), its what I had in my hand and my training took over when the guy tried to punch me.
But while that sort of thing just left me (after the suspect was in custody and the next morning) with a broken flashlight and sore wrist, I imagine the guy shooting the Barrett from the hip or offhand from the shoulder would have had one heck of a bruise later to show his buddies. Jeez, that would hurt!
I think, though, that if materials technology could develop light weight materials that could withstand the stresses of a powerful heavy caliber gun like .50 or 20+mm, and the proper design of body armor or a uniform could incorporate some sort of padding to absorb and spread the recoil - like a gel pack or something, then big caliber battle rifles would be more practical.
The real impracticality beyond weight (handling and carrying), recoil (that's obvious - specially if a quick second shot is needed), is the weight of the ammo. Right now I'm holding here a full 30 rd 5.56 mag and comparing it to a full 30 rd 7.62x39 AK mag and while they don't feel all that heavy by themselves, hauling around 10 of these things plus the rifle adds up. Just imagine what hauling around high capacity 20mm or .50 mags, plus a gun that weighs around 25 pounds or more would be like - brutal.
That's one reason I figure IMTU LAGs and most other high caliber CPR guns use at least caseless ammo and/or jacketed ceramic rounds that fragment on penetration.