I'm not sure what the right solution is, but this is pretty gross as you describe it. Off the top of my head, the only thing that would make me feel better about Flattr is if they somehow tracked money as it flows through Flattr, and prevented double-taxing content creators.
I do find my perception interesting though. Generally, I'm pretty pro-company in the sense that, they need to pay their devs, they need to pay their bills, investors, etc. Yet, if a company moves itself in my head to the "we're here for the community" side of the line, suddenly they conceptually become a non-profit in my head, and if their profit feels like more of the pie than absolutely needed, it feels like the worst type of greed. Greed from the needy, greed from those we're trying to support, etc.
If the money then circulates then that's OK. If the money is withdrawn then take a good cut of that.
One downside to that is that the more popular it becomes, the more 'currency' the flattr-coin becomes, it simply circulates with people neither depositing it nor withdrawing it. However, flattr are then effectively become a central bank and that isn't a problem.
The real problem with not taking a cut of moving between flattr accounts is that people would sell flattr through side channels to avoid flattr taking a cut. So you'd pay me cash and I'd transfer to you the flattr coin on platform.
And if it took off in a big way then money laundering becomes a problem and the cut would not cover the cost of KYC etc.