seo – Dynamic Serving via ‘vary http’: Is still valid? Why the industry prefer full responsive websites instead?

I have a client that asked me to develop a website using a dynamic serving technique, basically he uses the vary http header in order to serve different versions of the front-end discerning them based on the user-agent of the client.

So for example a light version could be served for mobile devices, where a heavy one (with more CSS) could be served to a desktop pc browser.

I’m sure that this technique could be a good solution, for example I can prevent a mobile device to download css with media queries that it won’t use anyway, and also avoid to download parts of html that I would eventually hide on mobile (Google says that it’s not considered cloacking as long as content data is similar).

But besides the duplicate logic, because in the long run you’ll need to maintain 2 different frontend views, so changes will always be twice (on the mobile and on the desktop version), I’m wondering if it’s still considered a valid approach, since I don’t found too much information (and not recent information about it).

Furthermore, I’m fully aware that responsive web development is a valid way to go but is my client right when he says that with responsive frontend the mobile device still needs to download the full css bundle?

Any suggestions or insights will be really appreciated!