I still use this strategy, though these days, I primarily use Mosaic and Netscape for testing. I tend to browse without JavaScript enabled, except for places I already trust to not abuse it. And if there is anything blocking me from accessing the page, such as a modal dialog, a cookie notice, a survey, a prompt to sign up for the newsletter, I close the tab. Over time, I have found that type of rude lack of considera…
Are there any version of Mosaic that are able to handle modern HTTPS?
Security isn't everything, there's also accessibility to think about.
HTTPS breaks in many circumstances when it's not needed, including on current browsers.
You can also use a stripping proxy.
Bigger issues I've encountered with actually using Mosaic is that a) it does not support the Host header, so you must have a dedicated IP address, and b) it doesn't like semicolons in then Content-Type header, which most of today's servers include.