The 30-06 has been winning 1,000 yard NRA matches since it's inception when fired in the 1903 Springfield rifle & Model 54 & 70 Winchester bolt guns.
If you attended Camp Perry, up to the middle 80's, the military furnished the ammo for the service rifles. Even in the match rifle category, you were required to shoot 30-06. You shot 30-06, or 308 when the M14 arrived on the firing lines in the middle 60's.
Most civilian shooters used the free brass for their long range loads. By the time you get into the 70's the majority of civilian competitors are shooting state M14's, only shooting Garands if they have to. When the civilian M1a came out, the Garand went out very quickly.
Something else that was true at the time, the only good match bullets were in 30 caliber. That began to change, and change fast, in the 80's. The last guy to win NRA week at Camp Perry with a 308 was Tom Whitaker in 1996.
The military stopped furnishing free ammo in the 80's, and almost everyone is shooting .223 in the service rifle.
Though I shot my M1a yesterday in our club 100 yard reduced course match. Shot a 480/500 with the thing. Still, the good .223 shooters all left me in the dust.
The 308 is used by the Palma group, but it is due to the rules. What has really taken over the 1000 yard line are the 6mm and 6.5 mm rounds. Things like the 6.5/284. The wind ballistics were always so superior, it just took decades to get them on the market.
I don't know what was the last year the 30-06 won a 1000 yard match at Camp Perry. It has got to have been a while. Maybe a civilian with a 30-06 Garand got into the shoot off's. A shooting bud of mine got into the shoot off's (Porter Cup?) around 2000 with a triple lugged Fowler 308 Garand. He placed second, behind a Marine shooter. The Marine he was shooting against, and the ones behind the line, were all pleased and surprised to find out that when my friend was in the service, he carried the Garand in basic, at Camp Lejeune!