But, in your number system where π is 4, what is e?
More to the point, we aren't just making up numbers here to enjoy infinite decimal expansions; the reason is that you can wrap the radius of a circle around its circumference more than 3 times (or, if you don't like numerals, as many times as letters in 'pie'), but fewer than 4 (not as often as letters in 'easy')—and no changing of units is going to get around that.
More to the point, we aren't just making up numbers here to enjoy infinite decimal expansions; the reason is that you can wrap the radius of a circle around its circumference more than 3 times (or, if you don't like numerals, as many times as letters in 'pie'), but fewer than 4 (not as often as letters in 'easy')—and no changing of units is going to get around that.