With PoW all that burned energy creates a strong root of trust.

How do you establish that root of trust with PoS? Currently approaches are ultimately circular, IE trust it because the majority holders of the coin are continually voting to trust it.

You need a good initial distribution.

With Bitcoin mining pools it looks like there's just as much centralization (if not more) as with proof of stake.

The difference being you don’t need to ask existing Bitcoin miners for permission to begin mining Bitcoin yourself. Conversely, staking is inherently impossible without first obtaining “stake” — and how can you obtain stake without the approval of existing stakers?

You don't need permission, but you do need money to buy mining hardware. Might as well buy a stake for that money instead. Same thing, isn't it?

> Same thing, isn't it?

US dollar payments aren’t subject to the approval of stakers, and existing PoW miners have no on-chain mechanism to prevent new market entrants from competing against them for hashrate.

So, “no”.

To begin staking, you first need stake. But merely transfering a PoS coin from an exchange to your own wallet for subsequent staking is inherently impossible without the approval of existing stakers. Even this isn’t enough: existing stakers must also approve of your initial staking transactions.

Which is not how PoW mining works.

PoS is something fundamentally different from PoW. PoS-like ideas were around since before PoW, but such a system can never be used in a trustless way, which was what PoW enabled.

So it's fair to say that Bitcoin could never "transition" to PoS since the whole premise from the start was that it wasn't! It could not exist before. Now that it exist, and has been shown to work, it has caused a cambrian explosion of sorts of protocols with less reliance on trustlessness. But they solve a different problem.