Also, I suspect Bitcoin at some point will migrate to Proof of Stake once aspects of that set of algorithms are addressed:
* Problems with bonding and checkpoints
* Problems with being fuzzily forgiving about slashing
* More rigor needed by doing rigorous proofs somewhere, in some way
* Some systems introduce a central party that rubberstamps the latest block (e.g. Peercoin)
* Existence of such a coordinating party costs the system its censorship resistance
* Since stakers have to hold funds in the system to author blocks, it's difficulty to have a fair launch of a PoS system. Many PoS systems get either started as airdrops, ICOs, or a proof of burn auction
* Staking requires some representation of the private key to be online at all times, which may mean that it is easier to redirect some of the staking power (in early PoS systems it had to be the actual private key, so not only staking power but actual funds could get stolen)
* Some systems require coins to have a certain amount of confirmations before being allowed to be used for staking, so spending funds interrupts your staking revenue
* Some people expect that staking revenue will be taxed differently than mining revenue
* Some PoS systems can be gamed for profit by trying a vast number of block candidates to cause the staker to get blocks more often than their stake should qualify them for. Such an incentive may turn such PoS systems just into PoW schemes under the hood
* Some researchers argue that "by depending only on resources within the system, proof of stake cannot be used to form a distributed consensus, since it depends on the very history it is trying to form to enforce loss of value".
These are not problems I came up with, they are from various sources, such as Bram Cohen.
For full disclosure: I have Bitcoin, Cardano, and Ethereum, in that order of holdings.