A lot of the engines have a “punch” parameter which the manual describes as “adds a compressor-like envelope, which accentuates and distorts the sound.”.
However, when I apply it it always sounds thin and distorted, as if the punch is taken away completely. Is this intentional or is something wrong with my unit?
Depends on machines…
Notice how it lets a sharp transient through, that’s the “compressor-like” envelope part.
Sharpness is obvious on CY ALLOY, distortion on BD MODERN…
Sometimes it is inappropriate and lacks…punch!
Might be that it just not always works with the wide range of interesting spots of the machine’s parameters (even the BD Modern).
Personally I just use it when it sounds good. But I like that the recent machines don’t have it anymore (Swarm, Sy Bits) and make room for actual sound design paramters 
I’m not a fan of it TBH, sometimes and on some machines it sounds OK but mostly it doesn’t really work for me. It seems to take some of the bottom end out of the sound somehow and loses too much of the sound after the initial transient.
You’re not wrong, and it’s funny that “Punch” often takes the “oomf” out of sound. Maybe this is because for some machines like the kick drums, it is simulating hard compression, and so you need to turn up the level to compensate?
A boxing glove. Smooth on the outer edges but carries a lot of weight inside(heavy compression and distortion). If its too sharp it wont be a punch. Look at the TE graphic on the OP-1 for Punch.
As always, if one asks different people what “punch” is (or any other of those vage and useless words such as “warm”), one gets a lot of different answers.
If “punch” refers to transients (which it usually does), it can’t be about the low end, because the low-end comes after the transient, especially on kicks (a pitch envelope starts high).
i remember liking this parameter much better on the model cycles than on the syntakt. my guess is they just ported it to syntakt without really thinking about it and then realized it sounds like ass without the cycles low headroom and that’s why the newer machines on ST don’t have it anymore.