I mean, you can, but you shouldn't. I don't think anyone is arguing that any representation is suitable for all usecases or that ieee754 should not be available in programming languages.
Also, I think I'm too tired by now, I get confused too much between the rationals as the rational numbers \mathbb{Q} and the rationals as an implementation of rational numbers using a quotient of two integers.
Also, I think I'm too tired by now, I get confused too much between the rationals as the rational numbers \mathbb{Q} and the rationals as an implementation of rational numbers using a quotient of two integers.