You won't get any compensation for this, hundreds have complained but it won't get you anywhere.

Court-ruling

In its latest decision (III ZR 48/17), the Federal Court of Justice has reiterated that passengers are responsible for their own schedules and must allow sufficient time for airport security checks. Under this court ruling, you have to face the consequences

What can be done?

All you can do is face the facts and next time arrive at the airport earlier considering the business of the airport.

Is Frankfurt airport taking kickbacks from the airlines for missed flights?

Highly unlikely. Believe it or not, airlines hate long and unpredictable security lines too. The FAA sets minimum connection times and when these need to get longer, the airlines lose operational efficiency. The airlines DO NOT control security and neither does the airport; this is typical supervised by a government agency.

Case in point: I recently flew out of Berlin Tegel where they still have one security point per gate. It was moving extremely slow and you could really see the airline employees imploring the security personnel to speed things up, and they even brought in a senior police official to look at the situation. In this case they needed to delay the plane.

So overall inefficient security harms the airline: it causes delay, unhappy customers, lots of extra work, and loss in operational efficiency. That's not easily offset by the few extra tickets they sell.

I missed my flight after standing on a security line for over 1/2 hour, then going through passport control lines twice.

Sorry, but you took a wrong turn or went the wrong way. There is no official connection or check-in in FRA that requires two security lines. To be fair, FRA is huge and somewhat complicated, so it's easy to get lost.

I've flown through many of the world's busiest airports, and have never had an issue like this.

Then you got lucky. While FRA can be bad at times, I have certainly seen worse. Last time I was in Taipei, there were 2000+ people in the security line and lines ran almost through the entire terminal building.