Personally, I can't really say that I miss any of the sites designed like they were in the 90s, with their ever-rotating GIFs, Flash-based intro pages, "Designed for Netscape" badges.
And does an influencer need to have his/her own website? Not more than an ad needs its own website.
The "original Internet" is still there, and I dare say more people are using it than back in the 90s. It's just that a lot more people are also using the newer stuff that you don't like.
And that's fine.