That's only useful in comparing subsets though and we need a way to compare the size of any possible pair or group of infinite sets, given that the bijection method makes way more sense. Even though it's slightly unintuitive to laymen how can one thing be larger than another if for every member of one group I can match them with a member of the other group, provably for all the infinite members of either group?

I get there's a conflict with intuition there but infinities an inherently unintuitive.