Does every chiropractors see babies?

A few. There is absolutely no reason for a chiropractor to ever see or treat a baby or child. Any condition they might go after in this age group should be handled by your pediatrician. It is shocking, and unethical for a chiropractor to see anyone that is not an adult. If an adult wants to waste time and money on a chiro that is their issue. Kiddies cannot make such a choice.
Should They?? To my knowledge there is no training program teaching a chiropractor how to safely perform manipulations on babies. There is no supportive data that it is safe to do this and no proof of any benefit. So be careful!