My guess is that whoever came up with the square root of -1 did so many years before it 'escaped' from mathematics and found a practical use. Before then perhaps people thought it was clever, but not necessarily useful or even 'true'. So then, if you need to understand electricity, and you can do it best by using i, then even someone who thinks it's silly to have a square root of negative -1 would have to grudgingly admit that there's some 'reality' to it, despite its unintuitiveness, because electricity behaves as if it 'exists'.
Seeing as how there was so much resistance to infinite sets at the beginning, even among mathematicians, I wonder has the math of infinite sets be 'proven worthwhile' by having a practical application outside of mathematics, so that no one can say it's just some imaginative games?
