Unless you really view them as waste product and its a major problem,I'd think hard before you move them.Unless every single issue was digitized,with all the special holiday issues,etc, maybe if they're burnt to dvds or thumb drives,.I'd organize and store them in time line order in totes or cabinets.
I have almost every issue of guitar one,plus all the other big ones at least from the mid 80s to current. I prefer real copies over internet digital subscriptions and there's many reasons why for me.
There is a ton of valuable info in those mags.Some of that info/ interviews/ gear reviews,etc the artists themselves can't even recall today.I am regularly pulling up back issues from my collection of certain topics, etc.that folks are asking for.
Starting mid 80s,every time my friends and I went to a music store,while lots of people walked right past the latest mesa boogie,jackson,Tom a,marshall,tc electronic, eventide, kramer,hamer,etc catalogs or product brochures stacked on the corner of the checkout counter, ( for free too) I'd grab one of each. FF to 2023..
Many of those brochures are highly sought after,even by some of the manufacturers themselves, they fetch big moola too. (mine are not fs).I have used all this stuff at presentations, for teaching,for research, for learning of certain topics that aren't found in any search engine,etc.
So anyways, my collections have proven highly valuable over the years for me and others ,that I'd wouldn't have otherwise had if the local dumpster had claimed them.Every body looks at it differently. Ymmv.