Here are a few arguments for print journals, some I’ve heard, and some I’d make personally. 

1. Accessibility. Print journals can make journal articles accessible through the mail. This may seem an anachronism, but it still matters. There are locations in the world (including in developed countries) where the most convenient means of receipt is by post; rural areas with limited Internet access and no central library come to mind. 

2. Interactivity. Print journals are still generally more interactive than their digital counterparts. You can hold them, make notes on them, record your impressions, and clearly index them. 

3. Curation of linked content. Each journal issue may provide multiple linked articles, which together tackle a question from multiple angles. This can facilitate better comprehension of a topic or encourage the reader to explore multiple facets of an idea. 

4. Disconnecting. You don’t need to stare at a screen and get on the Internet to read the journal. You can keep it analog, if you will.

5. Anticipation. You can look forward to receiving a nice package of great articles with each issue. Rather than an article or two a day, you can get a nice meaty hit of intellectually stimulating goodness. 

Of course, those 5 reasons may not be particularly relevant to a faculty department — maybe 3 - 5, but probably not to the degree that they would make a print subscription worth it. Specific to a faculty department? I’ve seen journals by water coolers and in reception areas, perhaps in the hope that they can encourage conversation or, simply, give visitors the opportunity to read about research that is relevant to the department domain(s) — not so dissimilar from academic posters that find their home in the department’s halls.