If you want to measure growth based on another variable you are allowed to do so, but for most algorithms I'm more interested in the growth of time according to input size.
https://en.wikipedia.org/wiki/Miller%E2%80%93Rabin_primality...
As you'll see they are using the number of digits, not the value of the number, because the number of digits is the size of the input.
You can find countless examples of this in literature. So this is not a 'personally-interesting' way as you assert.