Does the Apple iPhone (5s) support APTx? If not, why?

I Can't say why it doesn't, Apple licences Aptx for the Mac bluetooth. apple's iOS implementation of A2DP allows for an extension which uses the AAC codec which delivers a similar quality but requires the receiver tobe able to decode this codec. Since Beats uses Aptx in their Bluetooth headphones we may soon see iOS support it

since the post was some 17 months ago I suspect L i A has lost interest 😁