There’s no reason to have the quantize setting stay the same as the last project open. It should be saved with every project, in the last state that it was in. There are other settings that for seem odd reason don’t get saved per project – can’t remember them now, but Quantize is a major one. This is a good example of something that gets in the way of flow when you’re moving quickly between projects and need to maintain the settings such as Quantize which you last saved with each project.
And, as previously requested a zillion times, EVERY setting should be saved per project.