To answer directly to the question:"
Is the Performance of a DAC Linked to Cost?"
No!
Performance should be defined before I shouted NO, but .. NO
For the purpose of Digital to Analog Conversion the best DAC reviewed here, so far its the Matrix Sabre_X Pro (SINAD 121 dB) about $2400.oo for 3 times less and just one (1) dB, lesser SINAD, is the Topping (D90 or??/)at 3 times less about $800.oo. Both convert a digital signal to analog with the least amount of deterioration, measured on AsR so far..
Mola-Mola Price ratio to the Matrix' is 8; for the Topping' >15... Audible differences if level-matched? Inexistent
Now if we are looking for great performance and best features, nothing comes close to the RME; One of the best DACs, One of he best Headphones Amplifier, comes with a PEQ, has a superb variable loudness control, is by all accounts reliable, etc... You buy it, end of the DAC story, and of the Headphones amplifier, and 2-channel preamplifier stories, I believe it can even "do" RIAA equalizing for the people with Vinyl ..., You don't need an external EQ and the so important Fletcher Munson curves are taken care of. It is end-game.. whether you have a speaker or headphones-based 2-Channel audio system. The RME is the king.
Almost no competition.
To repeat: NO!!
Peace.
P.S.
For comparison sake. One very good, popular and extraordinarily inexpensive DAC is the Apple dongle, yes, the one that is also a decent headphone amplifier, is $9.95 and audibly transparent. It doesn't have any power supply to speak off , yet beats out a $15,000.oo dac.