I think it's a bit of a stretch calling stocks "property" as it all exists only as a concept. If a merchant sells you food, or hardware, or any real items, those have value to people and are a cornerstone to society functioning. Everyone needs supplies. A merchant has to make sure he has suppliers, judge what his customers need, establish a store or means to sell them, etc. He profits, and his customers get things they need. That's not what day trading is. Pressing a button to buy some stocks in the morning at a lower price, then pressing another button selling them in the evening at a higher price helps society how?
I mean it's ownership of assets and liabilities, which have to belong to someone. You're saying stocks can't be a legal claim on something of real value to people?
The point is day trading is just a manifestation of the ability to trade. If you ever want to trade stocks, even infrequently, you're using the same infrastructure as someone who's trading in their bathrobe. That's where the value is, assuming stocks do have value of course.