The tractor won't do any damage to the asphalt (if it is good asphalt, it will be hard).
It for sure solves the problem of tracking dirt (not just into the house, but the garage floor will be so much cleaner

).
The cons (I had gravel for 35 years, and asphalt for the last 10) are (IMO):
- Won't get the gravel worked up when plowing off snow, that gives good traction. The flip side, is the asphalt will attract more heat from the winter sun, and melt/dry the drive sooner than gravel.
- Expense after the asphalt is laid down, is getting it sealed every few years. And, after 10 years, it is now time to lay down another top coat because of shrinking and opening cracks. Also, a few areas that need to be ripped out and replaced.
- Crossing the drive with a new drain field line from the septic tank requires a section to be cut out and now replaced.
- Heavy trucks can sometimes be too much for the asphalt. With gravel, just didn't worry about them as much. The gas truck will make some "bird baths" the first couple years of new asphalt, from the brief setting while filling. Should have laid out some plywood pads for the truck to set on to avoid the bird baths.
- Asphalt is more expensive, even in the long run, but I like not having the dust and wet dust after a rain tracking into the garage (and yes, then into the house).