That's a good point. Here's the counter point. Machining back then was a craftsman standing at an end mill or lathe. Today that would be very cost prohibitive but that's not how it's done now. Today it's a CNC milling center programed to complete all the necessary machining. Replace forging with casting and you could have a superior Browning design from the past falling within acceptable cost parameters in the present.
Still wouldn't get it, I think. The premise, so I gather, is a weapon for military use. We're talking hundreds of thousands of units. Economically, you'd still lose out to stamping, polymers, or aluminum (which is easier to machine).
Wouldn't that be cool! A modernized BAR, firing 7.62 NATO, lighter weight, higher rate of fire. Who wouldn't want one!
7.62 NATO isn't an intermediate cartridge; it's a full power battle rifle cartridge. That's why many of the assault rifles chambered for it (e.g. M-14, L1A1, etc.) were made semi-auto only. Full auto fire was simply uncontrollable. I'd be more interested to see a BAR in .276 Pedersen, .280 British, or even 5.56 or 7.62x39. (It does make me wonder: if MacArthur hadn't nixed the .276 Pedersen, and the Garand had been chambered for that round, and if the army then also ordered BAR's in the same caliber for logistical reasons -- which could be significantly lighter as a result of firing a less powerful cartridge -- I have a suspicion that during combat in WWII, when the BAR gunners realized they had an effective assault rifle on their hands, maybe there would have been a push to get more of those in combat, and if indeed we might have seen most US infantry carrying them by the end of the war. A lot of ifs in that scenario, but it seems somewhat plausible.)
Another problem with the BAR for modern use, is that the bolt locks to the receiver. This means the receiver is a highly stressed component, and needs to be made of steel. This will bring the overall weight of your rifle up at a time when other designs are using aluminum, stamped steel, or polymer to bring weight down.
It would be very interesting to see what Browning would do if he were around to use today's materials though.