The solution is to develop sites with accessibility in mind. Use a screen reader; experience what ALL your users will experience. Experiment with various rendering tools to emulate color blindness.
There are even more tools to performance tune your website.
This all comes down to the site author taking the time to cater to as many users as possible. It is not inherently a problem with the use of JavaScript, or dynamic elements.
So, yeah, there are a lot of shitty websites out there. Folks that choose to deliberately cripple their browser are more likely to see these shortcomings.