Here's another question though

"Would I like this game more if I didnt have my cool item right now?"

Hard to say yes... But in practice the answer might very well be yes. Challenge in games is rarely something you directly ask for, you want the reward after all, but often the fun is in exactly overcoming those obstacles, and not actually the reward. In that sense encumbrance might feel bad.. but being able to grab every single item always could very well ruin part of the fun.

In the end games are sets of challenges presented in certain ways, and its just whether those challenges work well from a game design perspective.