I can tell you YES with difinity!
Working for almost thirty years behind counters full and part time I mount and sell 10x 3-9 scopes over the rest! Next in popularity are the 4-12 & 6-18. Then they MUST be 50MM or bigger!!! Like it makes a difference, if they only knew better optics in 32/33mm size will transmit MOrE light than a cheap or many mid quality scopes can form 50+ MM objectives.
GONE are the days when people bought a 4x and called it good. Actually fixed power in general are very slow sellers.
I do my best to show the attributes of a quality 1-4 & 2-7 scope, most feel they need more.
Personally I own more 2-7 scopes than any other. Of those 99% are VXII 2-7-33 with 3-4 1-4-20 Leupys. I do have three 3-9 because my beloved Mauser's need a longer tube or offsets and offsets make for a higher mount...
I have to admit, I do have two 4-12's, and one 6-18 variable. The 4-12's are on rimfires and the 6-18 on my 17 Hornet Varmint rifles. Needed, nope but its better to show the red mist.
Like BigEasy prefer 2-7 scopes on my hunting guns. They offer clear brite optics with plenty of power and light weight for the ranges I "should be" shooting at. I keep them on 3X 99% of the time.
CW
Two things to add after reading a couple excellent posts a d needing a "new" scope for my 22Mah H&R.
Like everyone, my preference in a scope comes from how and where I hunt. Also, I imeadiately answered in terms of hunting. On my Rimfires I have almost always WAY over scoped!
I do so on purpose. Never having had many opertunities for truly long range hunting shoots. I sufficed the tendencies by pushing the limits of my Rimfires. So big powered (cheapie) scopes are on almost all of them!!!
So a "over scoped rifle to me IS 3x9 or bigger. But to a guy who hunts say Montana, Wyoming or Alaska like our friend Roger. A 3x9 is probably bare minimum! Like say a 1 or 2x might be for me!
So to make this so what of a better laid out question. I will say I think scopes of 3x9 and smaller are all a shooter needs to hunt big game out to 300 yards adaquitely. Move that max yardage to say 700 yards and one could easily see the advantage of say 12x.
Another issue with these big powered scopes is like big powered binoculars. Too much of a good thing is or can be less useful. It's hard to hold a 10x or larger binocular. Big powered scope can have a lot of mirage on warmer days. Just a couple other points to consider.
CW