Why is there a coin cap of 45B and not for example 45M or 21M or 45.8B? What's the reasoning behind that?
One reason for billions of ADA rather than millions may have been to encourage adoption. Psychologically, people are more likely to buy something when it is perceived as "cheap", and with a large supply of coins, the value of 1 ADA is likely to stay lower, longer (in fiat exchange rates). It also allows people to own whole numbers of tokens, and larger amounts, both psychologically rewarding.
This is my own speculation, @gRebel shared the only official source I have seen.
A simple and rational explanation for this lies in the plane of demography. Now the planet Earth is a home for about 8 billion people. Based on this figure, in the future, everyone could potentially have 5-6 whole ADAs, not fractions of it, like many Bitcoin holders have. Psychologically, this is much more pleasant for the holder.