as a beauty salon owner - I can tell you - that it depends on the salon - and the treatment.

Even a "quick" eyebrow wax - can take ages if your baby is crying and you don't want to let it cry.
For example... say you arrived at the salon - they have allocated 10 minutes for your eyebrow wax - and there is another client after you.
Your baby starts crying.... what do you do? Do you let your baby cry for 10 minutes whilst you get your wax... or do you cancel your appointment - and pay for it - as it's not the salons fault.
You really can't expect a salon to wait around whilst you attend to your baby, and all the clients after you become late.

Some salons do not have the facilities to cater for prams.
Some salons are doing "relaxing" treatments (massage & facials) in the same area as waxing & nails... and although it's no-one's fault - there is nothing worse then paying for a relaxing treatment and having to hear babies cry.

At my salon (which I recently sold)... we did our relaxing treatments upstairs - and no-body every bought a baby to the salon if they were having a facial or massage or body treatment. Some people did bring their babies when they had waxing treatments - and if they were crying; the mother would let them cry until her treatment was finished. If there was a staff member available, they would often watch the baby at reception - but this was not often possible.