Imagine many entities have a shared database. You cannot trust anyone else but you have to add something. The consensus mechanism of the algorithm of your choice ensures that only good actors participate through sheer game theory. This naturally has a cost and you are happy to pay it. You have a lot of fun

cannot remove anything is a feature, it prevents people from changing history (imagine being able to undo all your outgoing payments)

And the reason you have to solve 5000 sudoku is by proving you have a limited resource, in this case processing power (and proof of stake makes it the money you have and skip the 5000 sudokus). Because if you are identifying people by a user account, there's nothing stopping 1 person from creating 20 billion accounts.

I do understand what blockchains are; my question is more to whether they are used outside of cryptocurrencies or not.

I do also like your explanation.

This is just plain wrong. Blockchain is not a synonym for cryptocurrency or proof-of-work.

Grifters ruin everything and this reply is a perfect example