That is way too arbitrary. Just because money exchanged hands at some point doesn't mean the transportation is a net benefit or should be encouraged and everything else discouraged.

Besides, I think the economy would be much healthier if everyone was riding their bike recreationally (healthy bodies, healthy minds). And a much bigger boost to the economy than a delivery truck driving 10 miles to deliver a $2 package.

That seems too easy to game, and the system might have low compliance. Who's to say when a person is joyriding vs commuting to work on a bicycle? If we're taxing based on the economic output (which we hopefully already are via income/sales taxes), does the time value of goods being transported now get included in the calculation?

Why? If a vehicle has high economic output, presumably the owner is already getting paid for it?

Sure, but we're talking about F150 type trucks here. Most people in cities have those for completely personal reasons and not for "economic activity."