The protocols were made open by necessity, not by design. The motive was to connect academic , government, and commercial institutions across the country, all of which operated on incompatible operating systems and data networks. However, the common man would not have benefited from this before 1993, as the government effectively operated as a semi-competent firewall against commercial content and the broader public. They even sued ISPs that permitted legitimate accounts from remotely accessing the net through PPP or SLIP protocols. Not even commercial news feeds were permitted until the late 80s.
The only Internet the common man interacted with is the one that began to flourish as the government relinquished control. The Internet since the mid-90s is and has been a purely commercial achievement.
I remember a few BBSs that offered email (done via nightly UUCP so slower than people today are used to) to the common person.
Because it was new there weren't really thought out mechanism for people connecting early on, but some did.
http://www.armory.com/~spcecdt/deepthought.html
I had a UUCP feed, by either late 1992 or early '93. Several other local BBSes had one, as well.
There were some early ISPs, like The World (Boston), that had IP access around 1991 or so. I believe they were connected through UUNet. I don't know if they were routeable on the NSFNet? "Commercial" traffic was supposedly prohibited.