All such (locational) prepositions are dative: unter, auf, bei, neben, etc etc, when used in this way. That is, when they are specifying a location, rather than a destination for the associated noun or pronoun. Maybe I've misunderstood your claim here, but case isn't tied to the necessity or otherwise of the associated information.
Because it's dative case. If you wanted to say "I crawl under the bed" you'd use accusative case: "Ich krabble unter das Bett". This might be helpful: https://www.thoughtco.com/two-way-doubtful-prepositions-in-german-1444444