Amusingly enough, my completely dumb pair of computer monitors (also made by Samsung, but before they started making things "smart") has a 6502-based SoC driving the OSD, and there is no perceptible lag at all.
These "smart" TVs seem to be based on ARM SoCs running at few hundred MHz to 1GHz+ and probably have more processing power than a high-end desktop PC in the mid 2000s.
I think it's all because of the software - tons of bloat.
A lot of places won't define performance requirements, as it's not their forethought to do so. They care about functional requirements, and if it meets those, then in their mind, their work is done. I've worked in several places (big names, too), that don't define non-functional stuff until after their beta is shipped and people start complaining.
I don't know about the American market. Over here (France), set-top boxen aren't so bad. And there are regular software upgrade; some of them even include games and apps.
If some of the credential checks are stored in a separate device (dongle, smartcard ), then it could take even longer.
How do you make something so brutally garbage, anyway? Some of these TVs take so long to register a button press you have to wonder if they aren't using a 6502 inside to power the thing.
The only experience that's worse is those set-top boxes the cable companies provide you with. The Amiga had near flawless, real-time response and these things refresh at, maybe, a few frames per second.