There's nothing there that is impossible without a blockchain. The steemit website might as well issue its tokens using a simple database. Running it on a blockchain adds nothing except a 'shiny new technology' feel.

And why would I need the tokens in the first place? Hell, why would I need to pay at all, given that there are free alternatives like Medium?

You don't pay, you gain money. Unless, of course, you're a company that wants to buy advertising space.

As a user (writer/curator), you earn tokens for doing what you already do for free in reddit or facebook. The tokens you earn are like altcoins, you can trade them for whatever you like.

The tokens here are essentially altcoins, like ether or bitcoin. How would that be done with a simple, private database?

The steemit coins, as I understand it, have little to no other use (unless 'speculation/gambling' is a use case) so they don't need to be crypto coins at all. Instead they could be magic internet points that are all accounted for and transferable on steemit's website, with options there to buy more or to sell them for cash.

That’s like saying bitcoin could be a Money table on my personal database. It’s not the same at all. These coins are unique, wont be tampered, work on exchanges, and don’t depend on you trusting the startup that created it.

Indeed, that's the key difference. Steemit coins inherently require trust in steemit, since without the website's existence, the coins have no use at all. As everyone is implicitly having to trust steemit, there's no benefit in running a blockchain.

As you say, the key point of blockchains, like bitcoin, is that there is no central trusted entity. So, like steemit has done, if you add a trusted person or company, the main feature of the currency is wiped out and there's no point in having a blockchain in the system.

You needing to trust the website will exist for the coins to hold any value, while true, is not the same as having to trust the currency will work as a currency - i.e. that what is yours is yours, and the steemit owners can't simply wipe out the database or change their numbers arbitrarily.

I'm not saying this model is foolproof, and perhaps you're right and steemit (or app specific coins) will never be a big hit because of that. My point was just to show an example of a different kind of business model / monetization strategy made possible because of the blockchain, and there will certainly be others.