My take is that at this stage of the Brexit process it's primary benefit would be to obviate leaving with a no deal.
Like all these things there are pluses and minuses to everything.
Labour has wanted us to have A Customs Union, as opposed to being in THE EU Customs Union for some time. In terms of the benefits, the BBC website lays these out.
The Brexiteers in the Tory party and some of the Labour party as well hate this idea primarily because it would prevent the UK from negotiating separate trading arrangements with other countries. Something the leavers see as the big prize of leaving.
Distinction without a difference.