Buying non-KYC is nonsense. You can buy on Kraken and withdraw via Lightning to your real lightning wallet very cheaply.
Buying KYC is nonsense. You can buy on Robosats and withdraw via Lightning to your real lightning wallet very cheaply. Why give your personal data to Kraken when it's none of their business? Why give them the opportunity to track you whenever they might want to do so now or in the future? To me, that's nonsense.
Also, saying "No one cares to track when you buy" is obviously false with respect to Kraken, whose privacy policy explicitly says they track when you buy:
The information that we collect from you is as follows...Trading account balances, trading activity...your inquiries and our responses (“Trading information”) source
They also say why they track when you buy:
For the purposes of identity verification, compliance with court orders, tax laws or other reporting obligations and anti-money laundering controls...[And] To comply with applicable laws, subpoenas, court orders, other judicial process, or the requirements of any applicable regulatory authorities source
So please, none of this "no one cares" nonsense. They care deeply about when you buy, how much you buy, where you send it, and what you do with it; they log all of that info to the best of their ability, and they report it to governments who ask for it and partners who purchase it:
As part of processing your personal data for the purposes set out above, Kraken may disclose your personal data to any members of the Kraken company group, and to third parties. source
I recommend fighting back with Robosats -- which is easier and cheaper than Kraken anyway.