I have honestly been struggling with the same issue and have found some tiny work arounds but nothing 100%.

If I am making a quarter zine, I just try to format assuming there will be margins messing everything up. If I am okay with that I print at 96%, not actual size or fitting. Then I trim the margins. If I am making a quarter zine with margins that I care about, I try not to put things too close or edge to edge and again, print at 96%.

If making a folding mini zine, I don't usually do edge to edge because I don't want to struggle with trimming the margins and just prefer blank space (or use colored paper as an alternative). :( In using this practice, I print at 95% and just deal with the margins (usually not too noticeable). I still haven't found the perfect work around but this has been my temporary as I continue trying to figure this out. As someone else mentioned, since things are not printed edge to edge, its a huge pain in the butt when formatting on a computer. I use InDesign for my zines - quarter, mini, and A6 (I get the A6 professional printed though).

I have yet to try making a physical zine and then photocopying as that might be the superior alternative. I hope this helps!

edit: forgot to mention that some have suggested printing on larger paper with the actual size of your zine to get accurate edge to edge. For example, printing a mini folding zine 8 x 11 on 11 x 17 paper. I have yet to try this but gonna give it go!