Is there any reason not to go up for promotion?
Not really.  Promotion is primarily about pay (though sometimes the pay increment is small) and recognition of your achievements to those who are not already aware of them.
You are unlikely to get more duties after promotion because you are expected to take on the duties of the higher rank in order to get the promotion.  It's seeking a promotion, not receiving one, that causes you to get more duties.
As you already have a permanent academic position, a change in rank will not make much difference to your mobility; it is already very low.