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If they just block your account due to an automated process run by bots/ai. No customer support, no one to tell your story.

Very much this. I see users getting locked out of Google account often, or Google changing their policies (like the recent change of free G Suite accounts to premium ones) which would mean you'd be locked out of most accounts.

Are there big email providers, maybe paid, where potentially should be more reliable. Meaning at least they have a customer-service and you will not get locked out by the script?

I've heard good stuff from ProtonMail. It also adds a lot of security to email, if this of concern to you.