I also have ADHD and have an adoration for old-style website design. Not necessarily the 2008 - 2013 era (which I like to call the 1970's of the web), but websites before that which were more cluttered and unrefined.
Websites from the old days surface far more relevant information on the first fold than do contemporary sites, which I believe have gone overboard with Swiss Style design inspiration such that they think empty space is always preferable. The fact that many websites today use extremely large fonts in order to pass accessibility tests also doesn't help, but this is partly subjective because I personally hate reading text greater than 16px.
Maybe I would think differently if I did lots of heavy reading, but that's hard to do these days because most prose on the internet is filler and total rubbish. If I want to just find something, a website being designed like a magazine cover really doesn't help.
Allow me to illustrate my perspective.
This website, which has been online since 1994, would today be considered one of the most poorly designed sites of all time.
http://amasci.com/
Bask in the dark repeating background, the neon colors, and the quirky use of font size.
And yet, unlike 95% of sites online today, it loads instantly, and is organized such that I can find what I might be looking for without distraction. The author provides a header guiding new users to categories, and underneath is a list of links to pages the author thinks I might be interested in. And that's it. No Fontawesome, no TypeKit, no box shadows, no hover animations, no hover dropdowns, no sticky headers, no scroll jacking, no transparencies, no accordions, no hamburger menus, no bullshit.
A "modern" website would make the first fold into a glorified billboard, hide anything interesting in horizontal navigation of categories that have to be expanded out, use 19px font for prose because The Google, a masonry type layout because CSS grid bro, a sticky header that annoyingly animates in/out, and one to three popup modals asking me to give them my email.