In the beginning of my experience, it wasn’t that computers had fonts so much as each computer had A Font, and that was how the computer talked to you. All of them were quite low resolution; blocky and bad.
Now I expect every character to be drawn in an appropriate, smooth, curved, and informatively differentiated typeface.
When did that change start, and when was it complete?
To a certain extent, it begins with Macintosh, the first widely-available system to offer a GUI on an all-drawn screen (rather than character cells) and the LaserWriter, a printer whose pixels were not visible without a magnifying glass. I didn’t own one of those, though. What I did own was a 80386SX, a 32-bit CPU with a 16-bit bus, which had an astonishing 2MB of RAM and a 130MB hard disk, supporting an extended VGA card which could manage 256 colors at 1024x768 resolution. We used to think that was hot stuff.
Word for Windows was the first software I had regular access to that could manage some semblance of fidelity to a typeface on screen (not high fidelity) and on paper (not bad, really).
Convincing screen typography didn’t really materialize until 2000 or so, when higher-resolution displays could show TrueType scalable fonts. Before that, anything I saw on screen was a poor imitation of a book; sometime after that, I started expecting a close match.