At the end of the day they will only shift yours through a trader anyway so will probably thank you if you dont part ex it..
Depends on the dealer but I believe most will want the p/x because they make big bucks though they obviously don't advertise that fact much.
They'll take your car, say for £9,000 and flog it for £10,000 making a grand. As part of that £10,000 deal they p/x another car for £8,000 and flog that for £9,000 making a grand. As part of that £9,000 deal they p/x another car for £6,000 and flog that for £7,000 making a grand... and so on and so forth until finally the bottom car gets p/x for £f**k all and goes to the scrap heap.
If there are 8 or 10 or 12 cars in the sequence they are making that many thousands out of this.