What's wrong with my IIR filter?
You should start looking at your filter. Judging from the frequency response, the outputs look like expected.

You have designed a filter with a lowly 10 dB attenuation in the stop band. I would not call that a "cutoff", more like subtle equalizing. The stop band is everything after your cutoff frequency, including the very far edge. An elliptic filter doesn't necessary keep "falling off".

You should be able to get much better than that with a 4th order elliptic filter, if you just want a 6 kHz lowpass filter. Try pumping the dB up to 11 60 or so. 10 dB attenuation is hardly anything.