Well, if sitting on asphalt is a bad thing, then I suppose I'm in trouble. My pop-up, all 3 of my previous travel trailers and now my 5er sits on asphalt at home. They've been sitting on asphalt for some 25 years now. The only difference right now? I use a board under one side of the tires to make it level now. We had the drive way resurfaced this last Summer and they put a 6 inch slope (25 feet wide) so water would run off opposite side of the house when it rains. The board keeps the trailer level.
But, if you are concerned about your trailer tires dimpling the asphalt, then just put a long board under the tires on each side and you'll be just fine!
Does asphalt or concrete hurt your auto tires? Just asking?