In my opinion, JavaScript is object oriented language, it achieves object oriented featured through prototype-based functions: as you said the class key word is syntax sugar. In my opinion, “never use classes” itself is dogmatic. Use the right tool for the right job. It may be that based on your particular style of coding and architecture you may not ever encounter a problem that requires the use of a class, but…never? Never say never.
By the way, Babel transpiles ES6 code so that it runs in older browsers. I don’t think that “it transpiles into this ES5 code” is the same as this is what an “ES6 compliant browser does under the hood”. It may be in the case with the class keyword, but I think you’re taking liberties with the nature of transpiling that aren’t true.