It's so much harder to pull it off with the huge range in screen sizes and resolutions. Back then you could make an 800x600 (or maybe even up to 960 width) design and it would work on 99% of the monitors (rarely did anyone have more than 1024x768).
I think the range in aspect ratios is the bigger problem. It's hard to get around without resulting in a nasty reactive design where everything keeps shuffling around as you resize the window.
Sure, very solvable nowadays with media queries, flex box, grid, screen width and height units, etc. These features didn't exist in 90s CSS.
But even though the tools exist today, it is still challenging to do well. Agreed that aspect ratio variability is a bigger problem (we can no longer count on 4:3 as the standard).
I have a 4K monitor on my desk with 100% scaling, and one of the things that always gives me a chuckle is maximizing a browser window.
Most websites just stop getting wider after a certain point, which is fine because you wouldn't want to read a line of text that long anyway. It's usually a column in the middle maybe 1/3rd of the screen.
The typical thing was a fixed width container table wrapped with <CENTER> tags. Then you set textalign on that table. Voilá your table fit all your content with a fixed size/aspect but would float center on the page of someone with larger than 800x600 or whatever minimum you designed for.
While numerous websites settled for a fixed width indeed (I think, this was mostly a US school of thinking), responsive designs were somewhat doable with table layouts. What you couldn't do was a general change of element order etc. (However, you could respond in JS using `document.write()` on first render.)
