For 99% of hunters with 308 Win or 270 Win, you'll likely see them with 3-9x40 of some brand or other. Has to do with the best compromise of diameter, length, weight, able to use, price, etc. Maybe some might go 2-7 power for the 308. And I am pretty sure most game is shot with 4 power or 5 power - the highest powers are most commonly used for "sighting in" on paper targets. As purely for "hunting" rifles. For many decades, a fixed four power would have been totally acceptable. A few of us use fixed 6 power. A few of us might use fixed 2.5 or 3 power on bigger shorter range boomers like 9.3x62 or 458 Win Mag. The smaller powers tend to be lighter scopes - less inertia - tend to handle the recoil easier - also lower powers tend towards longer eye relief. I think.
Might have to do with age, also - a younger shooter has eye pupil that can open to 7 mm or more pupil diameter. Old guy like me more likely like 4 mm. So divide objective lens in mm by the magnification - is the exit pupil of that scope. So a 3-9x40, at 3 power - has 40 mm divided by 3 = 13.3 mm exit pupil - larger than most humans use up - very large, easy to pick up. At other extreme, at 9 power - 40 mm divided by 9 = 4.44. So likely old guy like me does not see all of it. If it was a 3-12x40 - at 12 power, exit pupil is 3.33 - will be much "dimmer" view for everyone, compared to the lower powers. So a fixed 6 power with 36 mm front sense - exit pupil is 6 - more than my eye can use, less than a younger guy could use. Leupold VX-III 2.5-8x36 - at top end, old guy like me can barely meet that 4.5 mm exit pupil - likely can not - at same time likely looks small or dim to a young shooter.
Do not think that higher magnification will make you a better shot. Read up on small bore free rifle competitions - world class shooters doing 10 rounds into less than 1/2" groups - standing off hand - at 50 meters - aperture sights - no scope. That is what good looks like! Key issue is to get a perfectly repeatable sight picture - and next to be able to break the trigger when picture is just perfect - so a target shape that matches closely / repeatably to the reticle - when younger I shot many 3 and 5 round groups, many much less than 1", from sandbag rests at 100 yards, with a Weaver K3 scope (3 power) on a 243 Win. Have to be able to see a very repeatable aiming point - do not have to be able to see the bullet holes.
Is common to see a bench rest target with a heavy edged white square - when conventional cross hairs placed dead centre on that square, you see 4 white squares formed by the reticle - remarkable how your eye detects the slightest difference or change among them - so, in fact, aiming at "nothing", but aiming very precisely and repeatedly. Do not want bullets striking that square - that changes the view for the next shot. Is common in bench rest to be going for group size, not placement. Placement competitions tend to use larger black bullseye with scoring rings - shooter often does not see bullet holes at all - give shooter pretty much exact same sight picture for each shot.
I believe the various Elite series numbers names might relate to the power change? Earliest variables tended to be multiple of 3 - so like a 3 to 9, or a 4 to 12 power. I believe earliest "2 to 7 power" were actually like 2.2 to 6.6 power. Then came multiples of four - like 3 to 12 or 4 to 16 power. And so on - not sure how many multiples are available today - 6 times(?). I suspect has all to do with angles of internal cams and the distances that certain lenses move inside to get increased powers.