I find encumbrance is good for three things.

1. Parties that loot everything. The kind that will steal wooden doors from subterranean dungeons because "somebody can use the wood" and "any copper we gain from selling it is copper we didn't have before!" If you make them go through encumbrance rules, slowing travel time, for the minimal gain (no money, since the wood won't be in good shape, but maybe some kids are willing to share their lunch for having some material for a fort? who knows!), usually someone realizes it's more cost-effective to just kill goblins. So far, my groups have realized this between "get the useless crap out of the dungeon" and the "are we really carrying this back to town?" phases.
2. Parties that prepare for everything. The kind that know some ancient vampire lords require extravagant methods to prevent regeneration. Beheading, stuffing holy wafers in their mouths, buring the head in sand, then saturating it with holy water (so you need a container for the sand so the water doesn't seep out). The kind of players that would hear this rumor, then proceed to find a way to carry 5 jars of sand, with some white sand, some black sand, some yellow sand, some regular dirt, and some silt because they aren't sure what silt is, just in case. In reality it may be a wide variety of things. Sometimes the fighter wants to have 10 different weapons on hand so he can swap when he deems necessary. Sometimes the rogue wants to carry a bunch of shit to MacGuyver his way through anything. Encumbrance can keep it balanced.
3. Grittier games with travel. The cleric passes out from exhaustion, can the fighter carry him? Or do you leave the cleric and the wizard while the fighter and rogue hurry back to town for help? These are the games that count rations, and count ammunition, and pay attention to exposure rules for being in the sun or rain too long, and keep track of things and micromanage where other groups say "let's just ignore that stuff because it's tedious and that's not fun for us." Encumbrance goes well with those groups, I find.

If you want to balance your group before they turn into 2nd group, use encumbrance. Or run them through some other situation where they lose some of their gear (getting washed down a river can clear out some of the excessive crap they pick up while still keeping their weapons/armor and magic items safe).