Most investors don't hold their own keys anyhow, so this won't make a difference for most people.
But it's still important to have the ability to do so even if many don't feel a need to. If somehow that gets taken away and all that's left is exchanging on centralised platforms, Bitcoin will lose any purpose.
Most consumers don't have any practical way of getting at their private key (if there even is one associated with their account), and the entire point of decentralization is lost. This is like saying you can melt down your GOLD ETF and make some jewelry.
But I never said that Bitcoin has no purpose, only that much of its original vision did not pan out. Clearly Bitcoin serves a purpose, and investors agree.
And a public ledger is not very... private. My GMail account is more private than Bitcoin because at least there would need to be a valid court order to breach my private email messages. Bitcoin transactions can be triangulated by anybody on the Internet.
Bitcoin is pseudonymous (don't be confused with pseudo-anonymous), meaning your public keys/addresses are your pseudonym, and it's up to you to take precautions of whether to connect your real identity with the pseudonym or not. So it can be private but doesn't have to.
As for Google account - they can be accessed by Google themselves if they choose to, so not much privacy there.
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If somebody within Google read people's email, they would be prosecuted (talking here about reading it in the way that most would care, e.g. your specific emails to get at your own personal messages for a specific purpose). Put it this way, for all practical purposes, if you are not breaking the law, your GMail is more private than your Bitcoin transactions. If you send an email with GMail that you don't want your spouse to know about, you are safe, for instance. With Bitcoin that is a lot hard, and far out of reach for most consumers.