Plywood is extremely strong...I'm not a furniture engineer but I'd wager there's no way a person would be heavy enough to break the seat portion of this hypothetical chair if you used 3/4" plywood

Plywood is strong in some ways but it's not really suited for a stool with legs attached how he described. Especially 3/4" plywood. As the stool was used the legs would work themselves loose.

A decent hardwood (maple, cherry, walnut, etc) would be a better choice and you'd want 4/4 or even 5/4 stock.