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nothatsfalse

Oh God no! Not Square at least. They'll happily send your financial statements to random other people, then act like it's completely normal that they did that, and really weird that you're upset about it. Plus their customer service (for end users who buy products, not the merchants) is extremely adversarial. They have a really shitty chat bot that is the only way to contact them to get help when they screw something up. It's awful and very anti-consumer.
You believe incorrectly. If you want to use some other services for email, streaming, etc., you need neither an AppleID nor an iCloud account to use any of your Apple devices. They may ask you to enter or create one, but I haven't seen a case where there isn't a (small hard to see) way to opt-out.