Bingo. Two-way alphanumeric pagers (basically the sort of device the OP is wondering about) were a fast-growing product from about 1995 to 2000. The digital paging networks (eg. the Flex network that MobileMedia/Arch Wireless built) were massively more efficient than the cell phone system at transmitting text messages, which let the paging companies undersell the cellphone companies for that service even with the overhead of having to buy a separate device for that service. But those were your choices: buy an expensive two-way alpha pager and fairly cheap paging service, or pay through the nose for text messages sent on the cellphone network. At those prices, nobody has big market penetration.
Then the cellphone networks made massive upgrades and were able to fold cheaper text messaging into cell service. That started the ball rolling for widespread use of text messaging, and also for a huge crash in the paging industry. Eventually the tattered remains of basically every major paging service provider consolidated into USA Mobility, which is mainly back in the business of providing numeric pagers to physicians.
(I was laid off from Arch in 2002. Got to see most of this mess first-hand.)