the pump action Remington 760/7600 is popular in states with thick woods, hilly areas, mountains, etc (kina like lever action guns); let's say you sight in on a deer and as you go through your 'aim, hold breath, squeeze trigger' sequence the deer steps behind cover just and you need a fast followup shot without losing your sight picture...this is where lever actions and slide actions offer an advantage (so does semiautomatics, but they are not allowed in PA so I choose not to expand on them);
as far as the Remingtons go, recoil can be tamed by switching to a managed recoil load (eg: loads offered by Remington and Federal Fusion), installing a slip-on recoil pad, and/or having the stock cut and having a dedicated recoil pad fit and mounted (for the older ones with a plastic buttcover);
the way my dad used his 760 was to use a scope with see-through mounts (if the animal was so close that all he saw was fur in the scope, he lowered his head and used the open sights); he carried 2 loaded mags...not for tons of firepower but to have extra rounds to alert people if he got lost and/or injured my firing 3 consecutive shots several seconds apart (pre-cell phone/portable high power FRS radio days) in combination with a whistle...still a good idea as a back up to cell phone/FRS radio
my dad's is .30-06; as he got older and lost some weight his tolerance for recoil went down; I had several improvements made to his 760; I had a Limbsaver (older design) recoil pad mounted on the buttstock to replace the plastic buttcover; I switched his Remington 150gr CoreLokt load to Remington Mananged Recoil 125gr CoreLokt load...to me it feels like less recoil than a Marlin 336 shooting regular .30-30 loads; I bought a newer scope with a thicker reticle and brighter picture (from an older Redfield 3-9 x 40 to a Bushnell Trophy 3-9 x 40); I also replaced his older extruded aluminum see-thru mounts (which seemed to come loose every few years) to a Weaver base-rail (lock-tite the screws) and heavy-duty steel see-thru sights that clamp on the base rail;