I've always taken "server side is slower" to mean "slower to host" in context of web pages. Sure it may blow chunks to parse 10 MB of JS to click a button and leave on the client side but that's 10 MB of static JS served via dirt cheap anycast style CDN and it doesn't matter if you have 1 client or 100,000 clients you could host it on a single server's worth of CDN which doesn't have to worry about any client state ever (and for the tiny percentage of client state you do need to manage it might be hosted on a much smaller solution that handles just that logic).
I'm more of the classic take that the "problem" is performance has continued to grow meaning we get more stuff made faster but the tradeoff is it runs at the same speed. Client side or server side there is no reason the app needs 10 MB of JS logic to do its job it just made it quicker and easier to deploy to have it use 10 MB of JS logic. For some things like required government services this is a real problem but for most things this is just reality - how fast a piece of software is isn't the only benchmark software is made against, often not even in the top 3 things it's checked against.
I'm more of the classic take that the "problem" is performance has continued to grow meaning we get more stuff made faster but the tradeoff is it runs at the same speed. Client side or server side there is no reason the app needs 10 MB of JS logic to do its job it just made it quicker and easier to deploy to have it use 10 MB of JS logic. For some things like required government services this is a real problem but for most things this is just reality - how fast a piece of software is isn't the only benchmark software is made against, often not even in the top 3 things it's checked against.