So you're solving the overpopulation problem by hoping the "kids, grandkids" don't exist or are small enough in number that death via accidents creates the space for them. OK.

The corollary of immortality for everyone (without sci-fi spaceships or suicide/euthanasia) is either stagnation (more or less the same set of people existing until resources run out) or overpopulation (and prompt resource exhaustion).