Might kind of depend...

How old is the place? The air system- as in the furnace/filters and AC if you got one. Do you have any reasonable expectation that the previous owners cleaned the ducts at all? And how long has it been since the system has been run- if it's been shut off prior to your getting your new home.

Do you think you might want to paint the place, or it needs freshing up?

Does anyone have allergies to cats or dogs?

Duct cleaning is often something overlooked. If there's smells of anything, cleaning whatever dust/fur that might be built up in the ducts can help.

If you tend not to run central air much, or it hasn't been on.. might have been a while since the furnace has been fired up, or the furnace heat might make otherwise less noticeable duct smells come out.

If you want to paint/freshen up, it's better to have the ducts cleaned and your air system checked/filters replaced before doing so.

If you are putting effort like scrubbing floors, washing carpets, and cleaning walls and ceilings into the cleaning prior to moving- then yep, getting the ducts cleaned too is worth it IMO.

If you plan to do anything that creates a lot of dust (e.g., sanding drywall), wait until that is complete before cleaning ducts.

Cleaning the dryer vent is more important. That should be done annually if you use the dryer regularly. Also check to be sure that the duct from the dryer to the exit point is solid metal rather than plastic or expandable foil.

My son bought an old house that had been a rental for a long time. Since he has allergies he hired a duct cleaning service to clean the ducts before he moved in. He was there when they cleaned the ducts and he said there was enough hair removed to build a dog!