The shops where I get my groceries are about 3 miles away. I tow the trailer with my custom build Surly LHT tourer/commuter which is worth more than the entire stock of x-mart cheapies in the store and I constantly worry about it being stolen when its parked there.
There are several parks within a few miles from home where I take my daughter on the trail-a-bike. With the little one on the trail-a-bike I don't do more than 10mph or she freaks out.
My LBS is about 5 miles away. When I need something major done by the LBS like just recently when they overhauled my rear hub I had to run the back wheel up there on the trailer (towed it with my mtn bike) so it's a slow trip.
When I get my groceries I tow the trailes and don't do more than about 15mph empty and 8 - 10 when loaded full of groceries, so thats also a slow trip.
For all these mission profiles it seems to me that a cheapie x-mart bike would be perfect. I can just leave all the trailer attachment hardware bolted onto it and I can lock up anywhere without worring if it will still be there when I come out. If it gets pinched big deal, I can get another one for less than $100 - brand new with 12 months warranty even!