I’ll ask again, does a migrant entering somewhere else and simply invoking “asylum” make their entry legal?
I feel like my last reply addressed that, but since you are asking directly I'll be explicit. It does not make their entry legal. Their entry was already legal.
That's what I mean when I say it is up to us to guide them through the complex process we've set up -- they are seeking asylum which is a status we recognize. They might not know the proper legal incantations or arcane procedures for that, but they aren't the ones who invented those legal incantations and arcane procedures. They are refugees doing their best. They should be treated as innocent until proven guilty.
It is not illegal to, while acting in good faith, get lost in the bureaucracy, ESPECIALLY when that bureaucracy is designed from the ground up to be unmanageable in order to disparage your right, ESPECIALLY when your own personal circumstances leave your life at risk.
Sure, you can point towards people who clearly knew that particular point of crossing was not legal. And I will point to people who already had their proper rights disparaged without due process based on how much of a failure the "legal" crossing was.
If you're only using these words like "illegal" in a 100% legalistic framework, where we care about the letter of the statutes and not the actual rights and people the statutes assert and protect... stop. Don't do that. That's harmful.