You can't risk an auto-grab mechanic unless you deal with encumbrance. We've all seen the memes about a Skyrim player with a backpack full of cheese, skulls and weapons, picking up a lone flower and suddenly being too heavy to move.
If you can only carry so many items or so much weight, then picking and choosing what you carry is important. But by now devs should know that gamers are just going to pick everything up. You can never be sure when it's going to be important, right?
Extra points against the game if the only way to get rid of an item is to discard it forever. At least let players sell it for a pittance, they took the time to collect it, after all.
Sliding scales of encumbrance are one way to fix the issue – the more you're carrying the slower you are. But developers need to consider the most important aspect of the debate:
Does even having encumbrance make my game better... or simply more tedious?
Generally it's just tedium. If your game isn't survival horror or hyper-realistic, you probably don't need encumbrance at all.