Leased Lines
Leased lines are always at the bottom of each network, no matter whether they are made as twisted pair of galvanic coupled wire, dynamic amplified lines, fiber or satellite link. They may be switched or not and likewise independent of end point equipment (modem) being included (telco supplied) or not.
History Repeats
It may be a surprise, but public shared/switched lines are a newer development than private/leased lines. Even back in the age of telegraph and Morse code, companies built or leased lines for private use. This continues with teletypes and phone lines further on. After all, it was always cheaper for large corporations to connect their subsidiaries via a leased line than to pay for each phone call or telex.
Switched phone network only came after private and leased lines.
And as with earlier teleprinters and phones, private lines were built or leased for data communication. Installing data networks atop those lines goes back to the late 1950s/early 1960s - including switching - and was pretty standard in the 1970s. Of course, this was only appropriate for large(r) companies and organisations - as before with phone and telex. Dial-in was only a minority use case - and even those were usually only using the next local office.
At some point during the 1970s telcos started to offer higher level products than just leased lines, including high speed modems and virtual connections, generating additional business by taking off low-level duties from company installations.
So essentially everything we now associate with (internet-like) networks was there, long before any public offerings were made. And long before telcos saw a business model in offering communication networks to a wider audience instead of only leasing lines. They repeated the earlier development during the 1980s with small and mid sized businesses in mind (*1) - doing the same step as half a century before when they created switched phone access.
And the same thing repeated during the 1990s when companies like AOL built their own networks on top of leased lines - just this time for the general public. And like before with telex and phone and later data switching, telcos saw the market and added/opened their network directly to customers, eliminating the middle man, aka AOL&Co.
Bottom "line": Nothing new since the 1880s, just repeated cycles of broader availability, all built on the same base structure.
Size May Vary
To be clear,this is about use in mid-sized to large corporations, as asked in the question - not some 5 man store with a mini in some corner - also, it's from a time before PCs or micros in general became a thing, ~1980..1985.
As an example of a smaller installation in the early 1980s, we can look at the department I worked for when returning from service in 1981. It was a local service department of a 'reasonably' large hardware manufacturer. Our area was southern Bavaria. For our own business we used two mainframes - one production, one for development - and a backup in Munich. Another installation was in Augsburg, a city about 80 km west of Munich, connected with a leased line running at 19200 Bd. Other connections existed to several local offices around the state, all leased lines running mostly at 9600 Bd. A network spanning about 300 km East to West. Maybe relevant here, we had no real IT budget, so our hardware was over all some 5+ years old ... about the age when our customers dumped and updated theirs, so we usually just rerouted what otherwise had been scrapped into our basement (literally a part of the parking level :)).
Our customers in turn were banks, insurance companies, even more banks, a not-to-be-named car manufacturer and so on. They had state- and nation-wide networks which were way bigger than that little mentioned. When in the 1970s bank branch offices still were running batch services using dial-up at night, by 1980 most of their branches were connected with leased lines, allowing direct access to their mainframe systems - likewise operating of the back then spreading ATMs (*2). Even small banks with only statewide operations had a hundred or more nodes connected with leased lines.
Larger nationwide banks had 1000+ branches and multiple computing centers, all connected by leased lines - with speed going into megabit ranges, including early fiber and satellite links.
In 1983 our little 'private' network and its (two surviving) mainframes was finally allowed to connect to the company's main network. I mentioned already it being a 'sized' company. From then on we had true global connections, and all of that on leased lines all around the globe, as there were computing centers or at least communication nodes literally in 100+ countries. All predating the Internet, all without IP and at most a few PCs peeking in, camouflaged as terminals :)
Take Away #2: For larger and international companies data networks were standard and in wide use.
The latter is also a reason why the switch to IP and generic internet infrastructure did at some places drag until the 2010s. Why dump a working infrastructure and in turn acquire all the issues of an open network?
P.S.: At that point it's often mentioned that a boot full of tapes beats a T1 line, even on long distance. All true, but as so often, it's not so much maximum speed but throughput. Anyone who had the job to bring a tape with patches to Russia - or equally worse the US - will tell you that travel time itself doesn't matter compared with all the border (Russia) and customs (US/Europe *3) hassles. That in mind, sending a Megabyte offer a 9600 line becomes very fast and attractive.
*1 - Plus the usual amount of hackers ... err ... technophile early adopters - which they may not as much have had in mind :))
*2 - Nowadays 80% or more of those branches are gone, the ATM being the only leftover.
*3 - It's easy to forget what a mess of borders and regulations Europe was before the EU.
