It's not that many internet protocols are text based. In fact, if I were to guess I'd say that text based protocols are in the minority. For almost every text based protocol you see on the internet there are at least two binary protocols that people have invented to send the same or similar data.
But it's true that the majority of internet traffic use text based protocols. This fact is interesting if you assume that there are many more binary protocols than text but many more text traffic than binary. It means that most of the successful protocols on the internet are text based. Except for a small number of applications (bittorrent is one example) binary protocols tend to die.
In the early days of the internet, corporations tended to design and use binary protocol (MSN for example, not the MSN website of today, the original proprietary MicroSoft Network that was supposed to replace HTTP) while the military, research institutes and academics tended to design and use text based protocol. Part of the reason was that building and debugging binary protocols was hard and corporations can afford to pay people to do it while the military, researchers and academics were doing it in their spare time for no pay (most of the people who developed the internet had jobs not related to developing the internet).
When you're writing code on weekends as a hobby and are not paid for doing what you do you tend to chose the simpler solution - text. So text based protocols got used by more people than binary protocols.
But that's not the full story. Building a network is hard. Really hard. We're so used to the internet today that we don't fully realize what a miracle of engineering it is. Almost every aspect of the internet evolved out of a bug fix. For example, we use IP address instead of MAC address because it allows us to build routers with just kilobytes (or these days megabytes) instead of terabytes of RAM for the routing table. The more and more problems we tried to solve, the more we tend to prefer text based protocols to debug them. Once we had enough experience developing the low-level network protocols, when it came time to develop application protocols most of the experienced programmers and engineers tended to prefer text protocols.
From personal experience, I've worked for a company building routers and I've also worked for a company building telemetry equipment so I've got a lot of experience working with binary protocols such as TCP/IP, ARP, IEC60870-5-101 and DNP3. I've also worked with text protocols such as HTTP, POP3 and NMEA. I've also worked with binary data formats such as ASN.1 and text data formats such as JSON and XML. If I were to choose I'd choose text almost every time. The only time I'd choose binary is if the protocol is really low-level (then I'd implement just enough so that I can plonk a text based protocol on top or it) or the data is naturally binary (like audio files).