I wouldn't expect it's because there's a server call - I'm sure the developers are smart enough to have all the analytics and tracking be async in the background.

Instead it's likely because these days every aspect of the TV is implemented in software running on the TV's CPU. With pre-smart devices, changing inputs would just activate some discreet on-board electronics to switch the signal over with no latency. Now you have to wait for the processor to get around to it, and it's probably busy loading up a bunch of app launchers and other crap you don't need, and doing some fancy whoosh-in animations, all of which is just getting in the way of what you actually want.