I think a lot of websites will still load at 100Mbps and 1Gbps in the far future since very fast web hosting is expensive, and most people just want to pay $1-5 a month for hosting their forum, blogs, and sites which don't need super fast hosting since websites are mostly text, pictures, and occassionally flash.
Flash websites are also unpopular because search engines can't read text on images, flash websites, so the rankings are very low for flash sites. Vistors also dislike flash because it slows down their PC and make sounds if the flash website has music and video, and they sometimes even block it with a web browser add-on like Flashblock, and NoScript.
More websites these days are also designed for tablets, and smartphones, so the website does not slowdown slower smartphones and tablets which can barely run a web browser at fast speeds.
A faster web connection would be useful if you share the internet with a lot of people who stream HD YouTube videos at once, or you download a lot of videos, and games online at once.