I did a test with a couple of my monterey jack. Cheesecloth lined some and not others. To me I couldn't tell the difference in the end. But to be honest they were only lightly pressed, and a soft cheese anyway.
However where I do think that cheesecloth is needed is to contain the cheese curd in the mould while pressing. I didn't line my alpine, because during the initial press the cloth stuck to the cheese, and I had to strape off the cheese from the cloth. But what I did have problem with then was cheese very thinly oozing from beneath the mould and from around the follower. When the cheese is cloth lined, it doesn't do this. I also have found that this problem is accenuated with the higher the pressure, (of course).
I know "they" say to keep tightening and straightening the cloth around the cheese during pressing, and Reg gave instruction a couple of times, as he got beautiful smooth pressing, but sadly I have never been able to replicate what he did. I still seem to get cloth marks. I really think that this is one area that requires practice to get it right.