Why does the eurozone want to keep Greece?

Because things aren't actually good for others either.(even the German economy, the economy in which the entire EU is organised to support(which is the first problem, economies 'in-service' is exploitation, and never constructive, always destructive), is struggling, and only making good numbers on Export, and low-wages, the internal boosts, like consumers, and spending are still in recession even, the living-economy, only export, and stock-markets are doing well).

And that is a fundamental problem, in normal economics your currency is a 'balancer', if things go really well your currency can rise with it, to limit overheating, but in bad times(which we're in now) the currency needs to devalue to reduce the pressure of debt.
And that's exactly what the Euro prevents both ways, so during the good times, it overheated the European markets, and now in the 'crisis' it's explosively growing debt(because all European countries, especially the ones using massive austerity measures have a ballooning debt, and nothing to slow it down).

That's why the economic-projection for Greece leaving is better(a GREXIT has a projected recovery of 1 year), than the projection of Greece staying in the Euro(they'll never recover, but come close to recovery in 20 years).

That's also why you saw the EU leaders opening the door for more negotiations after the referendum, the EU doesn't want living-proof that OUTSIDE is better than INSIDE, especially Spain is at a crossroads, where it's better for them too.

What the Greek government is doing, I'm not quite sure, they seem to have given in quite a bit, which would be a mistake, but with the Game-Theory they played so far, it could also be a tactic.

That's the key though, the EU is playing a 'Hotel California-scenario'(you can check-out anytime you like, but you can NEVER leave), and they're hoping the people believe it, because for now, and the forseable future, every Country in the Euro-zone would be BETTER OFF, without the Euro.

No one wants to leave today. If you get kicked, you must just kick back.

I honestly have no idea why. They'd be a lot better off without Greece sucking up their money & never paying it back.

It's the tip of the iceberg. So kick out Greece, next year you have to worry about Spain and Slovakia. Then Portugal and Estonia.

You also got to think these countries are watching. Kick out Greece and forget about collecting all this dept, meanwhile the local currency tanks and exports skyrocket as bargains. Sure maybe or maybe not, but Spain is likely watching going, it might be worth it to go our own and not pay our debts.

I don't think it is a matter of letting them leave. I think it is a mistake to let all these countries in to begin with.