Yep, that's my thinking. BUT, why when shopping for ammo, many times you'll see the same ammo, sold out of the 165gr but they have the 180gr. In the same ammo type of course and same price.
I've brought this up before. Why is everyone more impressed with Velocity? I know I can't outrun a bullet @1050 fps Muzzle Velocity (165gr), but I can't out run a bullet @ 905 fps either. Seems many will base their bullet choice based off of the Velocity, that faster is better. Just not true unless you're having a bullet race. So one is .08 slower to a 25yd target. A heavier bullet will more umph behind it all day long. So does that mean I always buy the heavier bullet??? NOPE. I also take into consideration of trajectory for accuracy purposes. I don't want one that is so heavy it has alot of drop due weight. Point is, it doesn't really matter how fast the bullet gets to the target. You're talking miliseconds difference. What matters is the energy and power the bullet has when it hits it's target.
It stems from a poor understanding of energy versus momentum, and which matters more for a bullet.
Energy = mass x (velocity x velocity) {can't make the squared symbol on my phone}
Momentum = mass x velocity
Mass of a bullet is of little importance in determining energy. So people think energy, and thus velocity, is crucial.
I do not agree, and I think momentum matters considerably more. For example, I could shoot a deer with a .17 Mag with very high energy but little momentum, and it's almost guaranteed to run off. But if I use a 12 gauge slug, with much lower energy and much greater momentum, the deer literally gets knocked off its hooves.
I actually think a lot of the acceptance that energy matters so much comes from our military equipping our men with a fast moving .22, telling them things like it's effective because of its high energy, among other nonsense like the whole tumbling round garbage - which would have to completely defy the laws of physics.
One valid reason for a lighter projectile is as you mentioned - for less perceived recoil. And Einstein explained why that's the case (every action has an equal an opposite reaction - so you feel the same amount of push at the buttstock as whatever is down range). A lighter round produces less recoil (all other things being equal), and delivers less momentum.