You don't need store bought weapons: Change my mind

I mean, given that you can basically complete the entire game using nothing more than the 1911 and AR-C (both equipped with suppressors, extended mags and reflex sights) even on Hard Difficulty, with the occasional use of the Compound Bow, M60 and RPG (all of which can be picked up for free in the game world) you really don't need to visit the store except for attachments and buying ammo/explosives.

The only weapon you even need to buy to complete challenges is the grenade launcher, since all the other weapon types for challenges can be picked up for free.

Note that I haven't tried infamous difficulty with the staring/game found weapons so it's variable (I always upgraded to the AK-M, M249, and Sa-50 before doing Infamous).