How to define project success?

The obvious answer is by measuring project success (i.e. scope, time, budget). Another answer could by measuring meeting projects objectives. I think the answer is not always straight forward. Lets have a look n some hypothetical examples.

Lets say you have a project with the objective to build a product. Your project is finished behind schedule and over budget. But the project was so good that exceeded the expectation so overall financially the profit was much higher than anticipated.

Your project is constantly ahead of schedule and under budget. But to achieve this status you pushed your team so hard so by the end of the project the best experts in your team are either burned out or had resigned.

You started with an unexperienced team, and you had bad estimates. You found the most efficient way to solve the problems, you worked on building he knowledge in the team and you always had a very good status reporting. You anticipated the delays and clearly communicated it to your stakeholders. But still, at the end the project was late.

My point is: you rarely are in the ideal situation and an absolute answer cannot be found. It always depends on the circumstances. Or, are this just excuses? Is the project success restricted to the triple constrain (scope, time, budget)?