I can't say I am worried about this.

I am not sure how the 'reliable with priority baggage delivery' airport will deal with it without the tags (hopefully they know from the bar codes) but by and large priority baggage tags have not ensured priority baggage delivery anyway, so I don't think it will make much difference.

I guess it saves a few seconds per bag for not having to put the tags on, and saves on paper and probably torn off paper flying around.