There are indeed libraries which have print or microfilm copies of those publications. San Francisco Public Library has a Periodicals floor where they can be accessed. They appear to have issues since 1995 (Climbing magazine) and 1998 (Rock and Ice magazine).
There are services which provide online versions of back-issues of these magazines, too. One such service is RB Digital Magazines, which again one can access via their online San Francisco Public Library membership.
That particular library provides services and membership (library cards) to anyone who shows up in person at a branch with proof of residence in the state of California. One doesn't have to be a San Francisco resident.
Since the San Francisco library provides these materials and online access, the answer to your question is "Yes", what you're asking for exists, and if this particular library doesn't suit you, I'm sure the same materials and services could be found at other libraries too. San Francisco is particularly modern and well-funded, so, libraries with similar budgets or endowments would probably be the best places to try. So, I'd suggest investigating public libraries in major cities, or, campus libraries at larger universities.