I have not run into cross-browser differences in a long time. That is differences, that actually mattered and for which I would have had to build any workaround. I have built several websites recently, using vanilla HTML and CSS and solved everything using server-side rendering.
What problems specifically do you see with server-side rendering?
From a security perspective I greatly prefer a client-server approach: you have an unsafe frontend where you care about ergonomy and aesthetics, and a backend which provides an API which handles the security.
Two different worlds and often two different kinds of developpers