My guess is that it has nothing to do with pre-2000 (or non-web), it's just that people enjoy a rote activity a lot more at the start of their careers when things are still new and interesting. When you've done 50 web sites, the 51st isn't nearly as exciting as the first ten.
I got burned out badly by a string of gigs that effectively came down to helping clients fight some self-inflicted business complexity and connecting yet another stupid website to yet another stupid database, but instead of quitting the industry I decided to slowly fire clients that wanted that kind of work, and build my own products. It took a while to get things rolling since I did this as a gradual shift, and financed it by doing smaller and smaller consulting gigs, but I strongly recommend that as an alternative to quitting altogether to anyone who feels the pain outlined in the the original post.
For me, immersive coding is an activity that brings a lot of joy. Building software is the closest thing to modern magic - you turn ideas, keyboard clicks and caffeine into something that people actually use; potentially making a positive impact on someone's life/work/day.
By building my own stuff, at my own pace, I rediscovered the joy of coding. As much as it was in pre-2000 work and before web.
If you build your own stuff, then there's nobody to tell you to connect a RSS feed to a RDBMS system. For me, the key to keep programming enjoyable is to be able to control the pace and business requirements. In my case, this translated to focusing on business-to-consumer products at a very low cost to the consumer, so I'm in charge of the product, not the customers. With B2B, especially at a high single customer price, people feel entitled to ask for stupid shit, and whoever manages the product feels compelled to accept it. With low average lifetime customer value, saying no is very easy. I assume that's not the only way to keep full control of the product, but it worked for me.