> Why should the browser contain a specific template engine, like XSLT, and not Jinja for example? Also it can be reimplemented using JS or WASM.

I think a dedicated unsupported media type -> supported media type WASM transformation interface would be good. You could use it for new image formats and the like as well. There are things like JXL.js that do this:

https://github.com/niutech/jxl.js