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Is it realistic/possible that the bitcoin core team make a new Bitcoin Improvement Proposal (BIP) on day in which they propose to change Proof of Work (POW) with something else (proof of stake for example)?

And yes, I know that POW was already part of "Satoshi Nakamoto's" paper Bitcoin: A Peer-to-Peer Electronic Cash System.

POW takes already more energy than smaller countries and it's proved that there are cheeper solutions (the existence of many alt-coins proves that).

Do you think, it's realistic? Maybe far in the future? Maybe without a hardfork?

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Chances of a replacement are very low. In fact, this is actually mentioned in the bitcoin community maintained wiki, which seems quite official.

See the "Prohibited Changes" list, where adding an alternative proof algorithm is listed under the "disputed" category.

Disputed: Adding alternatives to Proof of Work such as Proof of Stake. This could change core bitcoin too much, but with widespread agreement of some sort might be possible.

Note that they talk of adding, not replacing.

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Although some of this question is primarily opinion based, it raises some interesting ideas.

Firstly, there is no way to do it without a hardfork, because all blocks mined without SHA256 PoW would be invalid to old nodes.

Any hardfork is quite drastic, and changing the PoW algorithm especially, such a measure would likely only be taken if SHA256 was broken.

Note that PoS has many flaws and would certainly never be used in bitcoin. Likely that another ASIC-friendly PoW algorithm would replace SHA-256 if it was ever needed.

Also note that the energy spent keeping the network secure is useful in that respect, and bitcoin mining consumes less energy than gold mining, that's a common criticism which is quite unfair

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An idea I've seen floating around that would not necessarily require a hardfork is to add more mining algorithms as time goes on. Rather than switching to a new algorithm, you allow miners to use any of a number of algorithms. This could greatly improve decentralization since different hardware would be needed for each algorithm.

"it's proved that there are cheeper solutions"

It has not been proven there are cheaper solutions. Altcoins are cheaper because they're less valuable. Mining costs tend to approach the value of the mining reward + fees. A bitcoin block is by far the most valuable block out of any cryptocurrency, and therefore there are more miners putting more work into mining those blocks. Economics dictates that miners will compete until their net profit is 0 (in the economic sense that includes opportunity costs).

So until an alternative to Proof-of-Work is proven to be robust, no alternative will likely be attempted. The consensus in the community is that its unlikely that there is a way to do better than PoW, but of course that may prove to be wrong.

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