Wasn't it services like learn.to, beam.to and similar that came first? With the intend to have freely pickable shorthand URLs, where the shortness of them was just a byproduct?
I'm not sure of this, but iirc the learn.to/beam.to etc services were around in the early web already, mid-90s, while tinyurl and friends came later.
Those services were different because they were meant to provide an alternative URL for your website, not someone else's. Also, they required you to go through a signup process and I remember some of them displaying ads.
And of course, there was no Twitter back in those days to create an artificial need for short URLs.
I'm not sure of this, but iirc the learn.to/beam.to etc services were around in the early web already, mid-90s, while tinyurl and friends came later.