Over a hundred years ago, the .30-03 shot long, heavy 220 grain round nose bullets. It needed a 1:10 twist at the velocities they left at.
Three years after its origin, the bullet was changed to a 150 grain spitzer. It only needed a 1:12 twist to stabilize it. But the US Government in all its infinite wisdom decided to keep the 1:10 twist for that new cartridge they called the .30-06 'cause it was thought that would be OK.
50 years later when Remington designed the 7.62 NATO round, they knew a 1:12 twist was best for the 147-gr. bullet it used. Even though that bullet left about 100 fps slower than the .30-06's 150 grain bullet, it was still very well stabilized. In fact, the 1:;12 twist was better for accuracy. When the 172 grain match bullet was used, accuracy was even better with that slightly heavier bullet.
But sporting rifles had 1:10 twist barrels 'cause the public thought that was best. They knew the famous M1903-A3 Springfields had it and so did the M1 Garand. So it had to be perfect for the .30-06. But competitive shooters knew that a 168 grain bullet leaving at .30-06 and .308 Win. velocities was the most accurate with a 1:12 twist. A 1:13 twist is the standard for Palma rifles shooting their 145 to 155 grain bullets out at 3000 fps for long range competition.
So yes, a .30-06 with a 1:12 twist will do just fine with 165's. It may not be fast enough for long, heavy, bullets over 200 grains, but such is life.