That’s something you can write an entire book, or series, on. If you search back in the internet’s long memory, that exact question was being asked on forums all over the internet, and everyone will have their different answers.
For users, my TL;DR one-word answer is “dynamicness”, and by that I mean AJAX in particular. In the old days, websites ran on powerful servers that queried databases and did all the heavy data-crunching and then produced simple, light HTML pages that any computer could easily render.
Then Gmail and Google Docs showed up and suddenly everyone was like, wait, you can do all of that right in the browser instead of a desktop app like Office? That began an at-first-gradual, then suddenly explosive, fashion trend to move as much as possible into the browser, offloading work from the server and running it as a bloated Javascript app on each user’s computer instead.
In theory this means a more dynamic and “real-time” experience, like when you scroll down and the next set of posts load automatically without you having to click “next page”. In practice this creates all sorts of annoyances, like not being able to easily ctrl-F across the posts. And then Javascript itself got heavier and heavier, and browsers evolved to the point where they, not Windows, are really more the “operating system” today running websites as apps — and that’s really what they are, with hundreds of thousands of lines of code, not just document markup anymore. The desktop OS and desktop apps are becoming increasingly irrelevant. (Thankfully that is NOT the trend on mobile, where native apps are still alive and well and generally more usable than websites.)
Things like colored text were really just unintentional collateral damage that can be added to Discourse via plugin if desired (Discourse BBCode Color - Plugin - Discourse Meta), but that’s not really the resource hog.
But the reason, I think, many sites moved to Discourse was NOT for the end-user experience, but for the simpler setup and maintenance for the site and server admins. The old forums were often PHP-based, and at the time, PHP was not easy to maintain or secure or host, being the subject of both frequent attacks/security exploits and frequent changes breaking compatibility. It was a heavy “stack” to have to set up and maintain.
By the time Discourse came on the scene, they didn’t use PHP, opting instead for a mix of Ruby (a more modern, and in vogue at the time, web programming language) for the backend server and Javascript for the user-facing part of the site that you see. It is this latter part that makes Discourse “heavier” compared to a HTML page. Your browser runs Discourse as an complex app that manages its own data fetching, routing, click handling, etc., not just as an HTML page like in the old days.
Discourse was also easier to setup and administer, between helpful installation scripts, auto-updates, or in the case of the SDMB and other Discourse cloud customers, they just pay the company directly to manage all of that for them invisibly, and never have to deal with the underlying software.
Companies moved to what was easier and cheaper for them to host, without much regard to any user experience degradation that might’ve happened.
Outside of Discourse, the overall fashion trend towards browser app does make for the occasional truly interactive app that wouldn’t have been possible in the old days, like Figma.com (design), Photopea.com (photo editing), Felt.com (collaborative map-making), Airtable.com (lightweight Access clone), Canva.com (presentations) etc. But forums? They sit at that awkward boundary where either the old ways or the news ways would work. The new way is probably a little better on modern computers – arguably. But it creates more work for older computers that struggle to run the modern super-powerful and super-complex browser engines.
You can still find the old-style forums and use those if you want, but they take more setup and maintenance. And since the SDMB appears to be on life support, I don’t think you’ll have much luck convincing TPTB to move to a lighterweight forum anytime soon…