If this was not the case, there would be complete chaos and it would be near impossible to use multiple reputable exchanges at the same time in any sane way.
I think it's pretty acknowledged by now that various exchanges will treat your coins as tainted, even though some others disagree.
Those are old times, and old stories and most often those stories are missing key details. If one exchange supports coinjoined coins and another does not, that has nothing to do with AML/KYC issues -- those are exchange-related policies and internal risk paramters. Of course, differences in AML "data are" possible if you compare a fully regulated exchange (both in the US and EU) with some random yet popular exchange that is registered in Mogadishu. Additionally, an exchange can flag you for whatever it wants, it can flag you for having an username that starts with a B.
Neither one of those mean that properly regulated exchanges are not accessing the same AML risk data. I hope that this makes it clear now.
If you don't believe in the theory/research, then you can do the tests yourself with some tools assuming that you have money that you could burn as an expense to verify it for yourself.
I don't have the time, but I do have read plenty of cases, and that is enough for me to comprehend that basically each exchange buys from different chain analysis firms, and each database may often be updated, for example after a certain hack happens.
This is not true, it is based on a misunderstanding of the whole field. An exchange can decide its own risk parameters and other policies, that does not have any impact on the AML data. For example, an exchange can decide that any Monero swap coming from TOR or a VPN will automatically trigger an AML/KYC review. This again does not mean that it uses a different database, or that there is a "different" database. Many of the services even use the same providers to handle KYC, to whom you often also submit the AML data. Experimental testing over theory my dear, especially theory based on random user reports made by geniuses that have bought some scammed crypto for a discount and thought they could cash it out with a "no KYC" service.

We see a lot more on the AML side about people than people think, when you process countless millions of transactions you can figure out just about any pattern of behavior that an average person could come with -- yes, "they" know what those users are doing no matter how much people pretend that they are innocent in public.
How do you know? im pretty sure the top tier tools for these things have privileged information. On the other hand, like I said, you have no way to know how free services are doing it. In fact, im sure top tier ones work with Chainalysis and others and have updated cross-chain databases.
Experimental systems testing and sporadic access to Chainalysis. There is no logical reason for the top tier ones to keep information privileged, they are trying to sell their services to as many enterprise and institutional clients as possible. You are falsely assuming that these operate as some sort of honeypots, when they are just businesses built on evil ideas and like many other businesses they have an insatiable greed.
Never got around Sparrow Wallet. I think there's more risk in screwing up with a software you are not familiar with. I like seeing the complete list of inputs as seen in Coin Control of Bitcoin Core and just click whatever you want to use. If you label things properly it shouldn't be a problem. The accounts thing looks interesting tho. But multiple wallets is easy in Bitcoin Core now if you need that. If I have the time I will check Sparrow Wallet's account workflow and if it's good it could be suggested to Bitcoin Core and Electrum developers.
Accounts are one of the best features of wallet seeds, you really need to get around to learning it.
Could you mention what you think the best services are for each option? Were would b1exch and Trocador.app fall there?
I can't claim any services are the best, I can only tell you from the ones that I have experimented with what has worked for me in recent times. This is very different to users here, who will read some stories and then proclaim to know the truth about this service or that service -- which is completely false, and shows that they have no idea what they are talking about.
Someone might have a lot of issues with 1 swap service, while another person may be moving millions monthly through it. This is how things actually happens in practice in a half-regulated, filled with tainted coins and AML/KYC bullshit space. I have had the best success with:
Atomic swaps: UnstoppableSwap.
Decentralized bridges: THORChain, and derivative services built onto it.
Swap services: Simpleswap. This is the most dangerous category. A properly decentralized bridge will simply refund coins that they can't process, it will be done automatically. There can't be any freezing of any kind, which is not true for this category.
Trocador.app would be an aggregator but I'd put it into the swap services, this is why.
Transactions made through our website enjoy our Trocador Guarantee, if for some reason you do not receive your funds and the exchange does not provide us sufficient proof of unusually high AML risk or that it was blocked by their Liquidity Provider's AML system, Trocador will reimburse you up to the insured amount.
As for b1exch, it seems to be some kind of hybrid swap service that shows decentralized features but is also centralized. I do not have enough information on how it actually operates.
Keep in mind DYOR, and no guarantees. If something goes wrong with a particular service it is your responsibility. Pick a category and run some tests with small amounts yourself and see how it works out.
Depends on the context. Say BTC goes to $500,000 and you want to cash out some funds that are not KYC'd to buy real estate. Well, hiring a lawyer that has expertise in this field and has the top tier tools would allow you to produce a report that you can send to various compliance departments as needed. It's better than checking some random "AML checker" under a VPN or something. That's useful as a preview or funds you don't really need for anything relevant like paying for cheaper services, not doing a proper investment that requires big volume transactions. Like I said I really doubt you can compare these free AML checkers to the top tier ones which I assume have the most up to date databases that work with Chainalysis and have cross-chain information, plus if you are going to buy real state or something big you are going to be doxed anyway and would be best to work close with a lawyer expert in crypto and compliance, I would invest extra on this to produce the best report possible rather than use the free ones and send them to the CEX hoping you are not locked out and then hire a lawyer to try to send them a letter explaining how you acquired the funds.
You got the order of things reversed. How do you think these things happen unless you are using specialized off-boarding services? You send a message to a CEX trying to comply in advance? For them $500k is nothing, especially since you are not going to be trading with it. First you would send the funds to the CEX, and then you'd be proving things after the fact. Whether your reports come from a lawyer or they are compiled by yourself, that makes no real difference to them. You would not be sending them a result of a free AML check or the result of Chainanalysis in any case. For example, someone who has bought these coins on another regulated exchange could simply have a single self-generated document by the exchange. Where is the need for the lawyer? Very few lawyers in the world specialize in crypto AML, there are a few more that are low-quality services / scammers but go ahead if you love authority figures.

You can waste your own money on whatever your heart desires.
Those tools are only used for your own information in this context. You can check if some coins that you have received are tainted or have a higher risk, and then you can decide not to send those coins to a regulated platform to avoid a headache.