Yes, I have a previously crowned front bottom tooth than eventually broke off. It was filed down to gum level and a replacement tooth was added to my lower partial denture.
I would never have the roots removed for the following reaqsons. Firstly, if the root is sound it is possible to have a post inserted and a crown fixed onto that, this leaving the appearance of your own tooth but also the strength to bite on especially if it is a middle lower tooth.
Because I had a partial denture already, when a few months ago, two separate lower crowned teeth broke off on separate occasions, a new dentist sent me to have the roots removed at a special dental clinic. The result from that was my gums shrank back and altered the seating of the lower denture and I am now trying to sort it out.
Never have a root remkved therefore unless it is causing problems and ask for a post crown for that tooth.