Funnily enough, I believe that's completely achievable with enough time spent on it (probably a few weeks of an engineer working full time).
We have technology like WebVM [1] (from leaningtech / CheerP) or Copy86 [2] that already allows x86 machine code execution/emulation on the web. If you add an OCI client layer on top that is executable in the browser, it should be possible to run Docker containers in the browser.