I recently found out you can get foaming soap refills as tablets. I hadn't previously found a way to refill hand soap pump style dispensers without more plastic. These are from Meliora.
Invest in an electric one, which are ~10USD online. Electric ones have the foam mechanism near the electric motor, which is much further away from the actual soap, and hence avoids the design flaws in manual dispensers the other comments have already explained.
All the manual dispensers I've had, no matter how fancy, have consistently died before 10 or so refills.