How would a hard fork for a new key-pair/address generation algorithm be implemented practically? If an upcoming hard fork entails a switch to new method for key-pair/address generation, how exactly is it going to be carried out? How would all the old addresses going to change to ones that are compatible with the new algorithm and how is the transfer of ownership going to be conducted exactly?
For the blockchain to keep the same state after the fork, there would have to be a new address for each old (incompatible) address that holds the same amount of BTC and has the same owner.
One way I can think of is adding support for both the old and new key-pair/address generation methods temporarily, and then prompt all owners holding addresses generated using the old method to send their BTC to new addresses generated using the newer method, and finally dropping support for the old method. With ~30 million unique BTC addresses as of today, and a current block size capable of processing 2-7 transactions per second, this transition would need between 50-173 days to complete, during which the blockchain is completely incapacitated, and miner fees being higher than usual. I suppose it could also trap any BTC that hasn't been transferred to a new address by owners in a timely manner within the old, incompatible address.
You'd have both the old and new address types valid. You can't drop support for the old address types because there's no guarantee all coin users are going to convert their coins right away.
The updated wallet software, merchant services, etc will all only provide addresses in the new format though, so eventually the use of the old addresses will slowly drop off, just like how with the adoption of segwit, legacy address use dropped off (although not completely phased out).