The gemara questions whether one is allowed to use a piece of clay that has wine of a goy absorbed in it, since by doing so he is interested in the existence of the issur. The question is predicated on the assumption that it is forbidden to do something with issur hana'ah that indicates you want it to be in tact. The only question that the gemara has is when your interest is not in the issur, rather in the item that is holding the issur i.e. the clay, whether the prohibition applies. Although the gemara seems to be concerned that there is a problem of being רוצה בקיומו על ידי דבר אחר, it isn't clear if this would apply to things other than the special hadrayni clay. The gemara at the very end of the discussion makes a distinction between the 'cheres hadrayni' and 'kankanim'. The gemara says that the wine absorbed in "kankanim" - bottles, is not in tact. Tosafos questions whether this girsa is accurate, or should be deleted from the gemara entirely. Therefore, Tosafos concludes that if the girsa is deleted, we would apply the issur to other cases of a vessel that has issur hana'ah absorbed in it, whereas if the girsa remains we would not apply it to other cases. Two obvious situation would be a vessel that has either chometz or meat and milk absorbed in it, which are both assur to benefit from, would it be permitted to get some use from the actual vessel. Tosafos says that some poskim consider this assur, but Rabbeinu Tam who keeps the girsa in the gemara rules that it is permitted to use a vessel of chometz or bassar v'cholov to store something in.
The Shulchan Aruch (o.c. 450:7) says that one cannot lend a pot to a goy over pesach because the goy will cook chometz in it and the jew will want the actual chometz to be there since otherwise the pot would get too hot and break. This is not a case of רוצה בקיומו על ידי דבר אחר, rather a classic case of רוצה בקיומו of the actual issur. However, the Rama says that one can use a chometz pot to heat water for bathing and other uses, implying that he holds that we permit a situation of רוצה בקיומו על ידי דבר אחר by other vessels containing issur hana'ah. It is only by the hadrayni clay that it is forbidden since it is considered to be in tact, as Rabbeinu Tam paskened.