OG, I'll skip the part of your question re.: private property for others to chime in on.
As to the "forgiveness vs permission", that question assumes that "permission" was needed, to begin with. If that is a given premise and implicit factor, well then gee, go ahead and "ask permission". But the problem really is the question of : What places "NEED PERMISSION", is the real root of your question.
I never ask permission at public places. To do so simply presumes that permission was needed, to begin with. On the contrary: If there were no law or rule that said "no metal detecting", then presto, it's not prohibited. Why this need to feel that we "need permission" ? (as if our hobby were somehow inherently evil or dangerous enough, that it needed someone's princely sanction??).
Laws and rules can be looked up. No need to ask or talk to anyone. Lest you risk having someone say "no", when, in fact, no real rule actually said that. Because perhaps they morph something about disturbing earthworms, or "alter and deface" verbage, etc.... In other words: You risk the psychology of "no one cared TILL you asked" routine.
Just avoid obvious sacred historic monuments, and places with true "no detecting" rules/laws in place. At all other parks, schools, beaches, forests, etc... I come to, if they are public, I just go (barring a specific law/rule to the contrary).
As for the risk of "tickets" "prosecutions", etc.... I always ask the person promoting such a fear, to please cite for us any such incident, of this happening for routine innocuous parks, schools, beaches, etc..... where no specific rule existed. And rarely ever can any example be given. Thus if you ever hear of "tickets" "confiscations", etc.... it will generally be someone nightsneaking obvious sensitive monuments, or someone who can't take a warning, being obnoxious, etc....