If you care about precision - doubles still aren't precise - for currency use bigdecimals, for some stuff ratios can give precise results, for irrational things your only options are doubles, but be aware that you aren't precise, even for simply looking operations. No way to compute 10% of something precisely with doubles.
That's obviously not true. For irrational things, if exact values matter, use symbolic arithmetic.
For financial calculation you use a dynamic integer type that expand as needed.
I sort-of agree with you, in that it is easy to get bitten, and that if people have a dynamic integer type available on their platform that's probably safest. If the choice is between using integers for fixed point vs. using double's though, I'd go for the fixed point any day.
- there's a problem with how much precision you need. Different countries specify their way to round up doing money calculation differently (even with the same currencies - see Euro). When you use ints you have the assumption about precision repeated all over your codebase, which make it harder to change when tax law changes or you want to support other countries. With BigDecimals most of the code is universal.