If you don't need to see images, videos, it is not necessary to use a browser, and in your OP's sense, no browser is 100% safe.
I'm not entirely sure what this is supposed to mean. Viewing images and/or videos is not the only use for a browser.
In some places or companies the browsers are blocked, so sometimes if it's Windows(shit) I use MMC to find what I need.
I would not need to have privacy-enhanced browsing when using a company computer. I'm strictly talking about a personal device for personal use.