I'm of the opinion that carpets are something that you sell with your house. They're normally really well fixed down and will be a nightmare to get up.
So why do some vendors want you to pay for them?
It may be that they want to take you for every penny possible, or that they just really like their carpets and don't want to give them away.
This might be ok if they're new and in very good condition AND will match the decoration you want.
However if they insist on you paying for them you could
(a) insist on taking photos of them and the condition they're in when you agree to pay
(b) find out what sort they are
(c) find out how much carpet for the entire house would cost
(d) check under large items of furniture for any burn holes or rips.
(e) You could also refuse to pay for them and insist that any damage done in removing them is made good.
Removing carpets takes a lot of effort and is a dirty dusty job. If they're taking them to their new house then they have to have them refitted and recut so it's not quite a bargain solution for them - especially if it means them removing carpets that have been left. Taking carpets to the tips take s alot of trips for a full house as carpet is quite bulky.
If you love the carpets and don't want to have to fully recarpet then you might have to bite the bullet but insist on checking the quality of the carpet and insist that it's all removed if they take it up - else you'll end up with a house full of ripped up carpet!
Tell them you'll let them leave the carpets and dispose of them for them if they like but only if they leave them on the floors!
Insist on deducting the cost of a carpet clean if they make you buy them too!