If there is an SSPX policy by which their priests are giving the midddle finger to the families of dying Catholics, that is disgraceful (and a most grievous mortal sin directly repugnant to the priestly state).
Are you fricking kidding me???

A priest has a duty in both justice and charity to go to the aid of those in extreme physical and/or spiritual necessity, regardless of the disposition of the dying or their family, or what parish they go to.
It sounds to me like this policy is saying:
"Please don't waste our time. We have a lot of shit to do (although probably nothing to do when you call). But nevertheless, we are really delicate and precious, and we are sooooooooo overworked, that all these dying people are a real drag. Seriously, dude, can't you just go to the fαɢɢօt priest down the road? We thank you for understanding, and please be sure to inconvenience yourself for the next academy work day we schedyule for you. By the way, we also do online confession sign-up now, so we won't be inconvenienced in that regard either."
All that aside, I have had SSPX priests come to attempt conversion of my agnostic grandfather (and it will redound to that priest's glory that he attempted to convert him in his last moments, and may have even been successful). Another priest came for my grandmother despite the objections of jurisdiction made by the local novus ordo priest over her. The SSPX priest expressed some concerns about that, but when I said I didn't give a shit what the novus ordo priest said, he came and gave the rites.
So this policy flies in the face of my personal experience, and yet on paper it looks absolutely attrocious and unpriestly (and the horror stories from St. Mary's and elsewhere show that not everyone had as good luck with SSPX priests ministering to non-SSPXers as I did).
A priest (spiritual father) should be every bit as exhausted at the end of a day, as a biological father caring for his family is.