As other posters have already answered you: no, you don't need it.
You can even use ES6 modules directly in the browser, including import/export syntax. When I measured back in 2018 100% of our users of the company I was I was in had support for that. With brotli and HTTP2 the performance is comparable to bundled code.
The only holdover is JSX, of course, and maybe some things like the ?? operator that don't work in the client-side yet. But Typescript can take care of that. You can even tell Typescript to target ES6 so you can use ES6 modules in the browser, and this will let you eschew Webpack.
You can even use ES6 modules directly in the browser, including import/export syntax. When I measured back in 2018 100% of our users of the company I was I was in had support for that. With brotli and HTTP2 the performance is comparable to bundled code.
The only holdover is JSX, of course, and maybe some things like the ?? operator that don't work in the client-side yet. But Typescript can take care of that. You can even tell Typescript to target ES6 so you can use ES6 modules in the browser, and this will let you eschew Webpack.
So no, you don't really need Babel in 2020. :)