The problem wasn't the special mobile internet but the operating systems. Most phone OS before iOS just couldn't run full Gecko/Trident/WebKit/what-have-you. The phones could reach any external IPv4 addresses, but there weren't much to do with neither browser nor an app store.
You could run things like IRC clients, dedicated text chat apps, and server rendered browsers on live Internet. But downloading full webpages was too much for the hardware.
Yeah, everybody dropped WAP like a cobalt-60 source the very moment phones became capable of rendering usual HTML
For anyone else who is unfamiliar with Wireless Markup Language:
https://en.wikipedia.org/wiki/Wireless_Markup_Language
> Building on Openwave's HDML, Nokia's "Tagged Text Markup Language" (TTML) and Ericsson's proprietary markup language for mobile content, the WAP Forum created the WML 1.1 standard in 1998. WML 2.0 was specified in 2001, but has not been widely adopted. It was an attempt at bridging WML and XHTML Basic before the WAP 2.0 spec was finalized. In the end, XHTML Mobile Profile became the markup language used in WAP 2.0.