Equalizer doesn't work with Podcasts app at iOS 6! How to fix it?

Apple designed it to not work, there's no work around, and there's nothing to fix as it works exactly as apple intends. I don't know of any third party players that can access the equalizer controlls.

I don't think my next phone will come from apple.

They removed the functionality. With each ios or mac os update, apple removes some functionalities.

Workaround - use Denon. Though not as stable, it has music with podcasts in one place and it has (much more powerful than ios's) equalizer.

Delete the podcast app on ur device, you can then play all your podcast through the default player. The sound quality is much better.