> Most exchanges and corporations don't even go by a paper certificate,
Except the ones that do. You're right; most don't by default, but if you DO have valid paper certificate, it is a bearer instrument. Who owns it, owns it.
Which is to say, that the physical piece of paper is not a defining characteristic of property in stocks (even one case would mean that paper is not inherently part of stock ownership), just as physical stuff is not necessary in many other kinds of property.
Except the ones that do. You're right; most don't by default, but if you DO have valid paper certificate, it is a bearer instrument. Who owns it, owns it.