I'm sure everyone's seen "WTB Run of XXX, 20g, PST!" Let's look at this.
You're running an instance which there's no doubt that you can destroy. There are benefits to this, and there are drawbacks.
First, the pros:
1.) It's easy to do. Each mob will hit you like a wet noodle, and you'll hit them like a freight truck. If you can't one-shot most of these mobs at level 85, there's something wrong with you.
2.) You have a loot-collector. Just set it on "Free For All," and set the loot threshold to Uncommon. This will allow you to pick up greens, and you'll also get the silver drops. 5s from each mob may not be much, but it'll add up.
3.) Chance at enchanting materials. If you're an enchanter (or can group with one), instead of rolling on those greens, use the disenchant option. You'll get materials which you can sell on the Auction House or use to make enchantments.
Now, for the cons:
1.) It's not much gold from the trash. I know this was included in the pros, but let's be honest; you'll probably make 5-10g from the trash, MAX, throughout the entire instance.
2.) You can only do it 5 times in one hour. I used to have my friend run me through Scarlet Monastery Cathedral. It took about 5 minutes, and after a half hour, I was locked out. This isn't something you can do over and over, unless it's Blackrock Depths or a similarly long instance where it would take you at least 15 mins each time to clear (and 15 minutes is a fairly long time when you move from trash mob to trash mob, one-shotting them.
3.) It's much easier for melee than it is for ranged/casters. Okay, so this isn't really a "Con" or "Pro" per se, but if you're a caster, it will be slightly harder for you.
So to sum it all up, we're left with a decent amount of pros and cons. I'd say run the person if s/he's friendly, and you're bored. There are much better ways of making gold out there, but keep in mind that Warcraft is not a job, it's a game (PLEASE keep this in mind). You have to do what's fun, and if you're not having fun canceling and re-posting on the Auction House, then find something that is fun.