Sure, the "DVI" subset of HDMI generally works everywhere, although I've had signal integrity issues from cheap cables in the past.
It's all the other stuff that's supposed to seamlessly integrate your components. Audio Return Channel so sound makes it to the speakers regardless of where a source is plugged in, Consumer Electronics Control so you can use one Bluetooth remote for everything, automatic power synchronization, etc.
Even 4k is a little weird, with different HDMI versions supporting different frame rates. I have a Yamaha receiver from 2014 or so that doesn't support 4k, but claims to "support" it; all you have to do is turn off the receiver and it will pass the signal through!
It's all the other stuff that's supposed to seamlessly integrate your components. Audio Return Channel so sound makes it to the speakers regardless of where a source is plugged in, Consumer Electronics Control so you can use one Bluetooth remote for everything, automatic power synchronization, etc.
Even 4k is a little weird, with different HDMI versions supporting different frame rates. I have a Yamaha receiver from 2014 or so that doesn't support 4k, but claims to "support" it; all you have to do is turn off the receiver and it will pass the signal through!