I do something like that, but use pandoc to get whatever format they ask for. It's not always nice looking, but it's seldom me who is initiating the contact (ie they already have an interest in me, and they need a resume "for the process").
Similar, I wrote mine[0] with Typst (alternative to LaTeX) and YAML. It's source is still plain text but I get a nice PDF with the beautiful typesetting reminiscent of LaTeX and an easier scripting language.
edit: The generated PDF from the template mostly works with OP's resume-parser[1]. There's just fields lacking like Certifications, Awards, and Skills which are parsed under the Projects Category.
Disappointedly, lots of "resume uploaders" refused to accept my file, even as .txt.
Had to retreat back to pdf. Hard times we live in.