The ALPS one looks interesting, but large and complex.
The point is that it's a combined encoder and switches. Multi-directional switches only are less practical for quickly adjusting values.
I think an analog joystick could work if it had detents, and if you physically limited the movement to X and Y only, as mentioned. Would it be better than a simple 5-way control, or rotary encoder + two buttons, probably not?
I'm going to experiment a bit to see what can be done.
Properly using it may require some (relative) "dexterity", which not everyone may have, as tooki pointed out.
I don't think the fact it can go in both directions at the same time is a real problem. Pushing it in both directions at the same time requires more force and thus is not as likely to occur by accident as some may think. But that'll have to be tested. OTOH, in some modes, having both axes could be put to good use (if there is a 2-dimensional parameter of some kind).
The real downside IMO is twofold: first, being a bit unusual, so requiring some getting used to. A simple rotary encoder or +/- buttons, everyone knows how to use that. And second, as I mentioned, it may not be very comfortable to use vertically, and more adapted to horzontal panels/consoles or handheld stuff.
And, in any case, you usually need at least ENTER and BACK buttons, so those buttons would still be needed.
I have seen combined rotary encoder + switches, smaller and cheaper than the ALPS one and more adapted to handheld devices as well. The rotary part is usually flat and meant to be actuated with a thumb. So, not ideal for anything not handheld. Yes, something that looks like the last one timeandfrequency posted, although I've seen some that are a bit larger and probably more comfortable to use. But still, those are typically "flat".