Anonymity is not directly "paying secretly the vile guys that are going to shoot the POTUS" or something.  We then get into debates about how it is impossible to achieve "perfect" anonymity.

No, the point is much more down-to-earth.  The problem with an open ledger like bitcoin is that there is essentially no privacy.  The pseudonymity thought off by Satoshi is simply not resistent to chain analysis.  The "web" of transactions propagates too much partial real-world knowledge, and allows it to be turned into an almost complete breakdown of the pseudonymity.   This was probably not anticipated by Satoshi.  We're not talking about law enforcement, but about almost everybody who can acquire some real-world knowledge and spend some money/effort on chain analysis.

Very simply put, it goes like this: If you, Joe, pay me, I consider it a break in privacy if you find out that I used that money to pay Mary.  You're not supposed to know about my relationship with Mary.

Now, how could you, Joe, know that I used your money to pay Mary ?  Suppose that you, Joe, are a guy who has a bar, and that I'm a plumber.  I'm repairing the toilets in your bar, and you pay me.  Nice.  Now, it is not a secret that you paid me for that work.  I pay my taxes, I don't have to hide that.  But Mary is my friend, and for her birthday, I give her some bitcoin.  And now, Mary comes and drinks a coffee in your bar, and pays you with her coins.

You can easily see that the coins Mary gives you for her coffee, are two transactions away from the transaction where you paid me.  So you know that Mary got those coins from me.   This is something I think is private and you shouldn't find out.  But I cannot avoid you finding out that Mary has the coins you paid me with.

Well, unless I use a mixer.  But then we're doing "anonymity" again.  And we're not talking about shady business.  We're talking about privacy.

With fiat, you wouldn't know.  Fiat is much more private than bitcoin.  With cash, that's pretty evident.  If you paid me in cash for the plumber job, and I gave some cash to Mary, you won't know that this is the same cash.  But even with bank accounts that doesn't work.  If I got money on my bank account from you for the plumber job, and then I sent some money to Mary's account, there's no way you can know that when she pays you from her account, that those funds came from me.  Yes, law enforcement could find out the transfers if they subpoena the bank, if they suspect me to be a criminal.  But you can't.  With bitcoin, all that private information is out for everyone to grab.

That's where something like monero comes in handy: to restore about the same level of privacy as with fiat money.  Even somewhat better.  But not to pay the guys that will shoot the POTUS.  That's not what we're talking about.  

That said, there are also situations where a bitcoin like open ledger is what people want.  For instance, for charity.  If you give a donation in bitcoin to a charity, you want maybe to see what happens with the money.  There's no secret or privacy to be had with the account of a charitable organisation.

Well, depends.  Suppose that I'm the recipient of some charity.  Should the whole world know that I got some charity ?  That I'm a needy guy ?  On one hand, yes: the donors would like to be able to verify that I'm not some rich guy running away with the funds of charity.  On the other hand, maybe I would like some discreteness about my poverty.

But one can see clear usage of open, transparent ledgers.   But also of private ledgers with anonymisation.