Several decades ago, most hunters were still using "iron" sights, while a few were coming to realize the benefits of optical sights.
For many years, the most popular rifle scope was the straight 4x magnification with a 32mm objective lens. The main reason it was originally manufactured with a 32mm objective was actually simply because that was all that was needed.
Over time, manufacturing techniques with variable magnification scopes improved, and the more common configuration became the 3-9 x 40mm. With a little higher magnification, a little larger objective was also needed.
But rifle scopes had become something of lasting value, and people bore and tire of whatever they already have. There was a "market" for something "new & novel" as much as something "better".
Since then, imo, it's been more about manufacturers driving sales with misleading marketing, mainly that more magnification is needed, as well as larger objectives are needed (which CAN be the case with greater magnification).
There was a period of time when gigantic 50mm objectives on 3-9x scopes was the latest marketing rage! I guess, if you were night hunting under moonlight, there might be a slight advantage (hence, some primarily night-use military optics having larger optics).
Personally, on day-use hunting guns (day use including dawn & dusk),
I have zero use for a 10x magnification having an objective any larger than 44mm, or a 3x magnification greater than 20 to 24mm.
Since we don't (yet) have objectives that variably adjust from 20mm to 44mm, a great compromise is a 3-12 x 44mm, a 3-9 x 40mm, a 2-7 x 32mm, as well as a 1.5-4.5 x 20mm. Assuming decent quality glass, all will do well in low light, although you may need to use slightly less than the maximum magnification as dusk turns to dark.
Actually, I would put a higher premium on glass quality than the size of the objective, so long as you're in the ballpark of a reasonable sized objective for the magnification being used.
