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I think it's not like that in my opinion and just from my knowledge of the centralized exchanges we're talking about that collect kyc. And I also think that these platforms don't care if the amount you transfer to other exchanges is big or small, whether the exchange platform you're transferring assets to is on a top listing exchange or not.
As long as they don't violate their policy, your account on their platform will remain in good standing with the assets they have, especially if their platform is regulated compared to other unregulated exchange sites.
Basically every centralized exchange really cares where your funds come from - that's why they ask you to go through KYC as well as KYT. If the source of your funds is deemed to conflict with their terms of service - then your account may be locked and your deposits may be frozen. This is of course in line with their plan to prevent certain individuals from using their platform as a place to launder money, whether the budget comes from hacking or otherwise.
You may need to know about why KYC and KYT are required on almost all centralized exchanges - even local centralized exchanges have implemented these rules for all their customers. But of course - this will vary from case to case.