Eh, mortgage or no mortgage, your kids will have expenses on the house to cover before they can access everything - taxes, utilities, maintenance, HOA fees, cleaning up the place, etc so there is already a potentially significant financial and time burden to cover until they get access to everything and ultimately sell the place. For a lot of places, property taxes at that point may be much higher than the P&I - and depending on the timing - may need the entire amount quickly. Many banks actually are fairly understanding with this as well, especially credit unions where a lot of my mortgages are.
If your kids are in a good spot and/or financially reasonably savvy, I don't think having a mortgage is going to make difference in terms of paying but may increase their inheritance. Plus, you can setup your mortgage payment to be autodrafted out of your bank account which should continue after your death.
That said, as a person with elderly parents and a wife with elderly parents, I don't care if they leave us anything at all - I'd prefer them to spend their last time on their last day and enjoy their remaining years!