The 308 doesn't have the horsepower to go past 1000 yds. and make hits all the time.. When I shot 1 mile the 308 shooters gave up at 1200 yds. and they were pushing big bullets..
I think you need to Google 'Match Rifle', or look at the GB UK NRA MR page
https://nra.org.uk/learn-to-shoot/match-rifle/
MR matches are shot at three distances in the UK / Canada with 1,000, 1,100, and 1,200 yard stages. On the high elevation / temperature range Coonabarabran range in Australia, 1,500 yards is the max distance stage.
http://matchrifle.org/Ranges/Coonabarabran.htm
MR is an offshoot of Target / Palma Rifle, controlled like them and F-Class by ICFRA and like TR/Palma is limited to 308 Win and 223 Rem, although nobody uses the latter. Exceptionally long-freebore chambers, heavy bullets seated shallow and some heavy loads allied to long barrels are used. A major restriction on rifle spec is a barrel upper weight limit of 5.5lbs though. 2-MOA five-ring / 1-MOA V-Bull targets are used as per Target Rifle.
In addition, the GB F-Class Association has an annual 'long-range' meeting in its 8-fixture league calendar, again with 1,000, 1,100 and 1,200 yard stages at Bisley in Southern England. The 1,000 yard F target is used at all three distances, so the five-ring diameter is only around 0.8-MOA at 1,200 yards, 0.4-MOA for the 'V'. F/TR scores are shall we say 'down' on F-Open at 1,200, but most competitors will get through the 1,200 yard stage with few or even no complete misses unless the wind is 'hard' to read and very changeable.
I agree absolutely it's not easy making 308 shoot beyond 1,000, but it can be done with the correct set-up and the right handloads. Before today's uber-BC Bergers, Sierra MKs were the norm in British Commonwealth MR with the 190gn model surprisingly popular, although many competitors loaded the 200 or 220gn variants.