Getting 5V DC from a 7812 output in parallel?

I have this little phono preamp which has an integrated psu, converting 12-0-12 ac coming from a center tapped transformer, to regulated +/-12Vdc with a 7912/7812.

I need a 5Vdc in this chassis as well, so I used a LM2596 DC to DC converter I had lying around which I plugged on output pin of the 7812 and ground, in parallel, the 12Vdc is stepped down to 5Vdc.

I have tested everything and it works fine, the phono preamp seems to do its job and the little ADC on the 5V supply is working fine as well.

Is there any downside to this setup? Should I try to build a psu which will be also fed from the 12-0-12 AC in parallel to convert it to 5V dc without connecting to the phono preamp psu?

Thanks!