It's not - my reaction tends to be the same whenever I catch a reference (in fact this is the second time Mr. Mack got out the old 'driver - he did it in Wildfire
as well). A Doctor Who
reference collides with a fresher imprint though, considering it's actively airing and popular. It's perhaps a bit easier to pass over a nostalgic reference after all.
Who knows, perhaps the truth is this: Back in the 21st century a Starfleet engineer particularly well-versed in human entertainment of yesteryear decided to nick-name a favorite tool sonic screwdriver
in reference, and the name just kind of stuck.