"Watch TV" - it asks initially, "What input is the TV set to?" "What remote do you use to control the volume?" "What remote to change the channel?"
And from then on, it works. It doesn't cover all on your list, but it has the potential.
For example, I have a TV, a Bluray player, and an AV receiver. I choose the "watch a movie" task, it turns all three on, sets the TV input to the input the AV receiver is plugged into, the AV receiver to the input the Bluray player is plugged into, and then maps the play/stop/ff/rev/etc buttons to the Bluray player and the volume buttons to the AV receiver.
Every button is configurable, all the on screen menu options on the remote are configurable.
An example of something similar: Ubuntu can become as simple as a stone. It would still be too complicated because it doesn't come pre-installed on officially supported PCs. Not third-party-brand-no-ones-heard-about with tentative OS support. I'm talking about an official Ubuntu PC where everything is made to fit with each other. Me and you are OK with patchworks of software and hardware, bugs and weird command line wizardy. Normal people want appliances. Windows PCs are something people treat as horrible appliances, which they've sort of learned to tolerate and work with over a decade or more of training. It's like a fridge with a control panel. Normal people need iOS. Options and customizability are bugs, not features to most people. Sometimes some (but not most) people want more than just an appliance, but they still want the minimal complexity possible given their requirements. Buying extra remotes or installing another OS is really not what they want.
Downvoters: I dragged desktop Linux into this because I'm excited about Linux and because it's hopeless as a consumer product.
Another glaring problem is how it decides to carp about low battery levels right in the middle of what you're doing. When this happens, it ignores your input until you acknowledge the low battery warning. After you acknowledge, it completely forgets what you were in the middle of doing. As if that weren't all bad enough, the battery warning can come back at any time after you dismissed the last one, including immediately, one second later, etc.
I find myself using the individual remotes more and more often in the past few years. They are stateless, have excellent battery life, and are incapable of measuring their battery levels. They don't have any of the Harmony's bad habits.
Logitech isn't really the company to do this. Apple would be great. Their brand is perfect for this. Apple's brand is, as far as I've gathered, "open your wallet and we'll make your tech easy to use, trouble-free, beautiful and sure to impress your friends". Logitech is "that keyboard/mice company". Would you buy a TV and HiFi from Logitech?