The most important thing the baby shampoo doesn't do is disinfect or kill all the bacteria in your makeup brushes!! That's scary and potentially dangerous to you, especially those with very sensitive skin. It's also lacking in the conditioning department. Brush cleaner products are made for brushes so they have the necessary ingredients to both kill all the bad bacteria and condition the hairs on your brushes. Baby shampoo provides a little bit of conditioning but that should be the least of your concerns!
Over time the bacteria build up can transfer to your face and cause irritation on your skin and even cause you to break out in a rash, pimples or worse! Sometimes certain products are worth the extra expense. Food for thought.... :-)