It really could only work around the time it existed I feel. The internet was a lot weirder back then.
One big difference then from now is that you basically need a PhD in the Canvas API (or WebGL or whatever) to accomplish something a 5 year old could do in Flash. Web design was a lot more accessible. You didn't have to worry about responsive designs and fluid layouts. You could just position:absolute everything and that was kinda fine.
I think you might have some nostalgia goggles on at the moment. There's nothing holding people back from making "weird" web pages today, they can even make them nice and responsive. One of the better concepts around HTML and CSS was separation of data and layout.
It's trivial to have a "weird" position:absolute design with a break for mobile that switches to a more fluid layout. Desktop users can have their "weird" layout but I can still read the page on mobile and you can readily crawl and index it.
People moved away from design tools like DreamWeaver that helped make "weird" stuff and instead installed WordPress or some CSS/JavaScript framework that just bakes in all the "boring" fluid layouts.
You're not necessarily wrong about Flash in terms of design or creation but your search engine wouldn't be terribly practical if everyone was still using Flash for everything. Flash allowed content packed inside SWFs but also allowed fetching external resources. You wouldn't be able to index any of that unless your crawler executed the Flash and/or inspected all the URL references for external resources.
Flash created an inaccessible deep web just like today's JavaScript website-is-an-application "sites".
Don't get me wrong, I love the old web with quirky table-based layouts, "unofficial" fansites, and personal homepages hosted on forgotten university servers in a closet. There was a vibrancy that's largely missing from today's web.
I think a big change has been tools have become more geared for boring than the creative and people treat content on the web as a side hustle. Google et all haven't helped by favoring recency over other relevance factors.
One big difference then from now is that you basically need a PhD in the Canvas API (or WebGL or whatever) to accomplish something a 5 year old could do in Flash. Web design was a lot more accessible. You didn't have to worry about responsive designs and fluid layouts. You could just position:absolute everything and that was kinda fine.