Could you use both to good effect? Waterfall to make a plan, schedule, and budget. Then basically disregard all that and execute using Agile and see how you fare. Of course there would be a reckoning as you would end up building the system they want rather than what was spec'd out.
You could. You might even say it's difficult to make any project estimate without your plan being waterfall. Planning and execution are deliberately two very different things, and convincing the customer - or the steering committee of that - is key to a good product.
These are all just heuristics that help people manage the fundamentally unmanageable: the unpredictable future. Everyone does a little bit of everything when working. A big company will waterfall year long strategies with the individual parts agile’d. Individuals will waterfall their daily tasks while working on an agile sprint.
