Currently Google takes all your data, bundles it up, and sells it to the US government (and basically anyone else willing to pay). The goal of these paid privacy services is not necessarily to prevent the government from getting your information, but rather to make sure the government at least needs to ask for it first.

There are few services that offer both anonymity and privacy, they do exist but nobody really needs that level of privacy unless they're journalists, whistleblowers, activists, or criminals.

There's also security reasons, having your messages out in the open unencrypted is a security risk.

There are services that allow anonymous payments. I think Proton, Mailbox.org, and Posteo all accept cash payments.

Kagi has a "privacy pass" feature, which uses some fancy ephemeral authentication tokens that are not traceable to your specific account. You lose personalized settings, naturally (like site rankings) but you can do searches that aren't directly tied to your account.

For email, there's no one-size-fits-all risk model. I mean, my email address is my full name, @ a domain that I own and is itself traceable to me. I have no need for anonymity, but I DO need privacy and security.

Is this more of an argument of privacy vs anonymity?

Exactly!
Privacy and anonymity are two seperate things. You can be post things publicly and be anonymous. You can post things privately to people who know you.

Having your credit card would prevent anonymity, not privacy.

The real question is what you’re trying to accomplish and why.

That informs your choices.

Privacy, security and anonymity are different things.

bitcoin isn't cheap

Well, you dont have to buy whole digit BTC (or any other cryptocurrency), you can convert like €50 into the wild and sketchy world of unstable currency which will be around 0.0026436362 BTC, but is enough to cover the cost of the transaction. I'm not sure I recommend it, only that it's technically not expensive because you're still using the equivalent of your currency, with a transitional currency.

things like search that limits options

And you can self host SearXNG, metasearch engines are much easier to handle than search engines, and I believe they are private enough -- no tracking or sign in data is communicated through each search API -- but I do not know all there is to know.

I guess when you pay with a credit card, theres limited information being shared. Taking things at face value, you are paying for a service that wont track you, see your data, give away your data etc.

Looking at it in terms of privacy vs. anon is a good way to look at it. If you want anonymity, you won't be using a credit card I assume, unless it's a throwaway you can top up. I imagine people who want full anonymity would be using stuff that's more specialised and niche than the likes of Proton etc., likely FOSS stuff, home servers, services without login/registration.

Privacy is like a step away from anonymity in that regard I think.

I think the primary use of a paid Proton or similar situation is to deprive the advertising panopticon of that data, not the state beyond the point of even an executive warrant, much less judicial. Your confirmation email from your dentist inherently deanonymizes the recipient as you, so you wouldn't want that to go somewhere anonymous, but you also probably don't want to feed the ad data beast by sending that to Google. It's no protection against the state, but the state can probably lean on your dentist if they care too much about when that appointment is, but using a Proton Mail combined with their aliases can deprive the private data brokers (who are the main source for low level ambient government surveillance) of a lot of information about you.