The risk of damaging a tire or rim beyond repair is real ... Knock on wood, i've not done that in many years and out others cars does not have room for a spare (i better update my signature....)
I've used such an emergency repair kit in the past on my motorcycle, but it is not something i would like to do in freezing temperaturs on a mountain road in a ski resort ... The same for the foam that comes with most skoda now a days that makes a mess .
So if the romoval of the very heavy seast is enough the tires stays - but could remove it if necessary.