Not nearly as weird as what you said. Since when is sales tax generally applied as a dollar amount? Why would we be paying a flat $10 per item? That makes no sense at all. That would mean a 10 cent piece of gum would cost 100x more, while a car might cost 0.05% more.
Practically all general sales tax is a percentage. A tax like this would be applied as a percentage, say 300% (and I remind you, this is completely unreasonable). That means that a $3 ice cream would cost $12 with tax, and a $6 ice cream would cost $24 with tax. So no, the better item wouldn't suddenly do better in the market. (Quite the contrary, the market would be racing for the bottom trying to sell crappy $0.25 ice cream so it would be $1 with tax, hoping to increase demand to the point that sales would again be profitable.)
a certain class of product (Veblen Goods [wikipedia.org]) is actually more desirable based if sold at a higher price.
Ice cream, being nondurable, is not a good candidate as a Veblen good. The same applies for most foods.