Interviewing and joining a higher level in career ladder

If your organisation is not promoting you, what can be the possible reasons?

Here's a bunch off the top of my head:

1. You're not performing well enough (obvious).
2. The promotion is very lagging - This video covers this concept in-depth.
3. Your org has a promotion cap (only X amount of people can be promoted each cycle), and other engineers took the slots for whatever reason.
4. Your manager doesn't like you.
5. Your company just under-levels people in general. A lot of companies are pretty infamous for this: Google and Amazon come to mind, particularly with their L4/SDE 2 promotion to L5/SDE 3.

Does it make sense for one to join another organisation at a higher level or is it a recipe for failure?

I assume by "organisation" you mean company. It would be a bit weird to switch within your company at a higher level. That being said, it depends - If you're currently under-leveled, you could be fine. But if you're fairly leveled and you negotiate an up-level switching companies, especially if it's a high-performance company like FAANG, this could easily be a recipe for disaster. Level expectations are not standardized, so it's hard to tell whether you would meet expectations at your new higher level at a new company. It's all pretty anecdotal - I have a "tier list" of companies mentally within my head based on my experience and what I've heard/seen from colleagues.