There was a time when only institutions were on the internet. Eventually one could get dial-up connection to a commercial entity. NYC's had an early commercial service provided by PANIX (Public Access Unix) and the San Francisco bay area had the Well.
This was just a terminal connection where one could connect to other hosts on the internet through a dial-up connection. The modem would connect to a computer that had a route to an internet gateway. PANIX provided a Unix user account one could dial into. One didn't need an IP address to get on the internet. The difference was that an internet host couldn't find/connect to the terminal one was browsing on. There was no "addressability". If one downloaded a file from the internet it didn't end up on the machine one was using. The file ended up in a directory on the computer one was dialed into. The second step of retrieving the file involved downloading the file from your home directory on the Unix machine one was dialed into. In my case I think I needed a modem that supported the Zmodem protocol.
Eventual the dial-up providers were able to provide IP addresses using the SLIP (serial link IP). Once one had an IP the machine was on equal footing of all the other internet hosts. The computers could exchange information directly. This provided an easy way for a web browser to directly connect from the machine one was using and the host one was connected to. This is when graphical browser became available to everyone with an IP address. The graphics became inline and could be rendered directly on the client.
I believe there were ways prior to this to inline render graphics I never experienced them. AOL used to be a closed network with graphics and no internet gateway. CompuServe may have been similar. I never used either of those systems.
Outside of my college's library connection I only accessed the internet through PANIX until the internet boom. I learned about PANIX through an ad in the back of Computer Shopper.
Mosaic, the first graphical browser was developed by National Center for Supercomputing Applications. They were of course not bound by dial-up or similar and probably didn't care for commercial offerings of connectivity in their priorities in development.
And before it, slip had been available and standardized for some time.
I would say what drove the adoption of commercial services was the graphical web, not the other way around.