In many/most cases, the family isn't in dire need of support from the missionary. In fact, they are more concerned about the missionary losing a family member and how the missionary will deal with the death, than they are about needing the missionary's support at the funeral.

In our mission it happened to about 5 missionaries and none of them went home. Truly, the Lord did bless us with strength to carry on and progress in the work.

If you're missing anything it would be just looking at the cost benefit aspect. For most missionaries (but not all), they're strong and they put their heart into the work even more — that's one of the benefits of not going home.

If a missionary does go home for death in the family it may well be even more difficult for them to regain their focus when they return to their mission. There may be people back home that would tell them that they shouldn't even return, just stay home. It opens the door for further issues that wouldn't arise if they just stayed out. Issues like bringing back homesickness, making it more difficult to jump back into the work upon return, possible loss of progress with or totally losing investigators, problems with traveling alone, various temptations along the way, . . . . etc. There really are a lot.
Those are/could be some of the costs. For me, I got over it and I was most definitely blessed.