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(Personal interest: I'm a Brit working in the UK for an American parent company)
Chief Justice Roberts brought this issue up on his dissent on the Obergefell vs Hodges case few years ago. The constitution never addresses the topic on the legality of gay marriage and thus the court should not be the vehicle for delivering that decision; that responsibility falls squarely upon the legislative branch.
The constitution did not address interracial marriage either, and yet Loving v Virginia was a critical piece of liberation through litigation (and very similar arguments apply!)