Game-dependent sure. But even your most action-packed table-top adventure is going to be hard-pressed to collect as much loot in the span of an hour as Diablo or Mass Effect gives you in a matter of minutes. Your DM also in most cases is not going to force you to waste time creating inventory for old loot/garbage weapons, which many cRPG's go out of their way to encourage.
The characters simply don't pick up that loot. Much like in TES games - most of the loot is left behind, uncollected. As it should be.
Picking up everything just because it's there is dumb. Which makes games with auto-loot extra dumb.
The thing with loot, though, is that there should be useful items all through the world. The mistake comes in expecting players to collect every last thing. What CRPGs should do, I think, is severely limit inventory, but offer tons of loot. In a tabletop game, a decent GM would enforce weight limits, and make you deal with the wagon caravan of +1 swords you're hauling around everywhere. Feeding those pack animals gets expensive, and sometimes kobolds shoot them with poisoned arrows. really, carrying all that loot isn't worth the trouble.
But that doesn't mean it shouldn't exist. Because you never know when you might need something.
Quite a few cRPG's are designed with that style: Baldur's Gate, Fallout, Elder Scrolls. The "no direction, do whatever you want" has quite often been a selling point for many of these games.
My first CRPG was like that. Questron offered no direction at all until you'd managed to gain a level, and then the only direction was when you spoke to any merchant, he would say, "Mesron wants to see you." Mesron was the King's court wizard, but the game contained no accurate maps (and no maps at all outside the castle), so even if you wanted to go find Mesron it wasn't clear how you could do that.
I loved that game. Someone should port it to Android or something.
Your DM is not going to stop you going West (except when he does, which feasibly speaking he can do since he's the DM, but ideally he'll get creative about it), but your DM is also going to be trying to give you relevant motives for why you should be dealing with the adventure, based on your character concept. And in many cases, unless the players are going out of their way to be difficult, they'll latch on to some aspect of the DM's plot threads.
The DM might also just move the content he had planned to the west, so you'll find it regardless.