That is exactly what we currently do, and speed of computations is definitely not an issue at all. If we have performance related problems (and we do sometimes), they have never in 10 years originated from numerical computation just taking too long, but always from other inefficiencies, quite often of architectural nature that uselessly burn a thousand times more cycles than the numeric part of the job.
BigDecimal provides exactly what we need: a no-brainer, easy-to-use, easy-to-understand and always correct vehicle for the calculation of monetary sums. It lets our developers focus on implementing the business logic, and also on making less of the described high-level failures that get us into actual performance troubles, instead of consuming a lot of mental share just to “get the computation right“ in all circumstances.
Hell, floating point isn't even a good way of doing imprecise arithmetic on larger numbers. What you would actually want is log arithmetic, but that's not what the hardware implements (even though it's simpler). It gives you roughly the same overall precision over each range but stops it from suddenly being cut in half as the exponent changes.
It is especially in cases like this that you absolutely should not use fixed decimal point systems to represent money. It is exactly in these circumstances that your fixed decimal point system will eventually encounter a situation where it fails catastrophically.
Intel provides an IEEE decimal floating point system specifically for the purpose of adhering to legal requirements, they say so right at the top of their website:
https://software.intel.com/en-us/articles/intel-decimal-floa...
If fixed point math would have solved this issue, they'd have provided a solution involving that, but fixed point math is simply the absolute worst solution to this problem, even worse than naively using a 64-bit binary floating point number.
BigDecimal is also a viable solution, but it's entirely unnecessary and the cost really is enormous especially if you need to handle a large number of transactions. But sure, if you say performance genuinely isn't an issue go with BigDecimal.