Definitely, AND no external , non clickable, requests either : webfonts, jquery, css, images, anything really. One such external request goes out, and we get a “AFE” browser : Access For Everyone, with the “Secure” part stripped out.
I suppose down the road there will exist two kinds of Safe browsers : one family that is HTTP clearnet disabled ( ie : there is no code inside to process http clearnet links ), sealed off from clearnet, with hardened and audited code. This family would passively handle security for users, and would be used in higher risk situations where security / privacy is the main goal.
A second family would allow both clearnet and Safe access, and would leave the responsability of security choices to its users : you are provided with a tool that can give you a secure environment, but you can open the fences if you want to, at your own risks. By mitigating security tolerance, this family would certainly help to grow awareness and adoption of the Safe network, with emphasis on the serverless aspect.
It should be be always kept in mind that Convenience is n°1 enemy when it comes to security and privacy.