> Why a "new currency"?

You need an all digital currency to keep transaction fees cheap, and to speed up transactions especially accross countries.

Just think about it, today's currencies are backed by physical paper. At some point, if A paid B, B should receive the physical paper money for the exchange. This is known as liquidity, and it's the major reason why money transfers over the internet today are expansive and slow.

> Is there a reason this is tied to the blockchain?

Yes, blockchain is key. Look at what all modern currencies in use have in common? They are backed by a very powerful entity, mostly governments with real power (weapon and authority on actual land and people). This isn't a coincidence, whoever controls the currency has huge power, imagine being able to make money as you please and give it to yourself or others.

You can't trust any single party with such power. Governments are the closest thing people can trust today, often because they have no choice, and sometimes because there's ton and ton of scrutiny, checks and guards in place around them.

And still, when currency is physical, it is also slightly harder to make more for yourself without trail.

Now if currency was digital, it be so easy to abuse, so anyone who had single central control could easily cheat everyone else. You'd not just be in control of the currency like the government is, you'd also become in control of the ledger. That means, that single central entity does not only control the digital currency (how much of it and who it gives it too), but it also controls the exchange of it (keeps track of who has how much of it and who transfer it to who else). That's incredible power, they could just seize your money without scrupule for example.

Blockchain is about solving this issue. If the currency and ledger is controlled by a distributed blockchain, then you don't have a single central entity with all this power. Instead the power is distributed to whoever wants to participate in it.

Now this is still an area of research in some way. Proof of work was one way, and it suffers from the fact that compute majority wins, and the compute majority could actually be owned by a single entity (which owns a ton of compute resources making up the majority).

Proof of stake is the new idea, it says that everyone who wants to be a part of controlling the currency and ledger has to put a deposit amount of their own money. If they are found to have cheated or acted wrongly, they never get that money back, otherwise they get it back and a little bonus for their effort.

In this scheme, you could still have a single actor taking full control, but they'd need to have a ton of money, more money then everyone else's combined stake. So it's much harder to do so.

> Is there a reason this would be tied to a company, instead of being run by e.g. a charity?

To some extent, it doesn't matter who starts it, if it ends up being a distributed open source piece of software, that is run by people from all around the world on different machines not all controlled by one entity, then it has become something out of the hand of whoever started it. Charity or Company, neither in my opinion could be trusted with a single central solution, but they can both try to kickstart an open source distributed blockchain ledger and currency, as long as it does in fact distribute control in a way that single or minority can't control it fully.

> I'm sure there are many issues with fraud/reversible transactions/KYC/anti-terrorism/anti-money-laundering that would need to be resolved somehow

This is probably one of the biggest issue currently, in a weird way, trying to solve the problem of no single central authority also makes it difficult for the government of any country to enforce rules and regulations over it.