Can Bitcoin actually get private transactions without a fork?

[ABCbits]

People who want privacy can use Monero, or creating their privacy coins by forking Monero, Zcash, or if they want to make noise: forking from Bitcoin and make technical changes.

They don't even have to leave Bitcoin to have some privacy. CoinJoin and mixer available if you prefer on-chain layer. Liquid network (one on Bitcoin side-chain/L2) also exist, although it's federated (not decentralized) and recently hacked.

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That reminds me, one problem I think the shielded pool has (and Zcash may have had) is chain analysis firms being able to label funds coming out of it as “tainted,” which means that people with clean histories won’t want to use it, which means a smaller anonymity set.

Regardless of what blockchain analysis service treat output/address that use privacy feature, the percentage of shielded ZEC coin increased over time. https://zecscope.com/charts/transparent-vs-shielded show today's percentage is about 29.1%, while 5 years ago it's only about 7.8%.

[ObeyKnock]

today's percentage is about 29.1%, while 5 years ago it's only about 7.8%.

Yes, the anonymity set did grow, which is cool regardless of cause. But an alternative explanation for this uptick is that NU5 was released in May of 2022, coincidentally at the beginning of the 5 year window you're looking at, which included Unified Addresses. With this release many wallets, such as Zashi, started shielding transactions by default.

It may have been that "people don't care about the taint label." But I suspect that a lot of that growth, from 7.8% to 29.1%, can be explained by "most people don't bother changing their wallet's default."

If you look at the percentage of shielded transactions since NU5 and see a continued, consistent increase in percentage after the initial NU5 bump, then that would be indicative of people caring less about tainted coins.

[Ashawowo(OS)]

And do you think Bitcoin should push further into privacy, or is that better left to separate coins?

This would bring a lot more trouble for bitcoin, it is already facing much controversy from strict regulations and outright rejections by some governments. I think it is too early to introduce this, if at all there is need for it. Privacy enthusiasts can use Monero, DAI e.t.c. I agree bitcoin was not created to be a privacy coin, pushing towards total privacy as at now is obviously a step in the wrong direction.

There are still L2 solutions that can help and bitcoin has privacy features like COINJOIN that people can choose to use.