If prop.test is an approximation to binom.test, why don't we use binom.test when computers can do it? When computing by hand, it makes a lot of sense to approximate the binomial distribution with a normal distribution because otherwise it would be impossible to perform calculations.
However, when using a computer to do hypothesis tests on a proportion, we keep using prop.test, which is based on the normal or the chi-squared distribution, which are approximations, instead of using binom.test that would give an exact result using the binomial distribution.
Then the question is why do we keep using prop.test instead of binom.test?
I can come with reasons to think that it doesn't matter much which one we use:

*

*Results are very similar for mid to large samples.

*When samples aren't large and results are (slightly) different, the power of both tests is too small to reach useful conclusions. Therefore, in real life, when doing inference on proportions samples are always large enough for both tests to be equivalent.

However, I can't come with a reason to prefer prop.test over binom.test when both are available and equally easy in a computer. Am I missing some reason? Or am I wrongly assuming than prop.test is routinely used when binom.test could be used?

prop.test is for comparing two proportions in two samples. binom.test is for testing a hypothesis about a proportion in a single sample.
Re-reading the help page of prop.test, I realise that it can also be used for a one-sample test, however I don't see why anyone would do that, given that (a) binom.test is precise and (b) prop.test doesn't advertise itself as method of choice to do this in the first place.
