A number of random thoughts come to mind. Apologies if this comes across as negative. I like the idea because it makes selling a hassle-free experience, but the way I am imagining it feels inefficient to me. "Free delivery" == $150 for a $300 couch? Or am I missing something? Does your truck sit for 90 mins during the auction? or are you making more pickups? If multitasking, isn't a truck a FILO storage for a FIFO process? Couldn't I sell on CL, get a bigger audience and hire a delivery/mover service if the buyer doesn't have a friend with a pickup truck? If a mover service is more expensive than you, then why? A quick search looks like I can hire a two man moving crew for $75 an hour.
The mean number of items in the van depends on the speed of pick up and drop off vs. the auction time.
If the pick up/drop off team is supposed to dismantle your bed/manhandle your new couch up six flights of stairs/plumb in your new washing machine, they could end up spending 30 to 45 minutes per job, so they'd only have two or three items on the truck at a time. So there could be plenty of free space if they pack it right. Then just staff the truck with two really strong people, who can lift a washing machine over a couch or whatever, and you've got almost-random-access storage :)
Assuming they're handling items in the $100-$500 range, i.e. their cut is $50 to $250, you could afford two guys even if they took 45 minutes per delivery - assuming you had enough demand to keep them working constantly. If they spend half their time on standby because of demand fluctuations, the economics would get more dicey on the lower margin items :)
If they get big enough, you can get vans with multiple side doors which would be more flexible about access [1].
It's an interesting point - cheaper items are not worth the time to the company to drive to pick up and subsequently to deliver, and more expensive items are not worth the cut for the seller, who can get cheaper pickup elsewhere.
Wait, I thought he was advocating that for more expensive items, its more expensive to find a someone to deliver/come pickup? In which, OP's idea works better only for expensive items.