A phone sends a message in a couple of seconds, so one handset comfortably covers a few hundred messages an hour — far more than most shops, clinics and small e-commerce operations ever need.
The limit is rarely throughput. It is availability: one phone is one thing to drop, one battery to go flat, one SIM to run out of credit. The second device is bought for redundancy long before it is bought for speed.
When you do add one, split by purpose rather than by load. Transactional messages on one phone, campaigns on another, so a marketing send can never delay a password.