Or, look at things from the opposite direction. Most cells die fairly quickly (in weeks to months) relative to the life expectancy of the organism (decades, for humans). This short life is probably terminated by the buildup of obstructive particles, such as plaques of misfolded proteins, to the point where the energy required to "repair" that cell exceeds the useful functionality that the organism could derive from it by keeping it fixed up. (The analogy would be a car worth $300 requiring a repair that costs $1000.) At that point, it is now "cheaper" to just kill that cell and replace it with a new one. And so this is how most tissues in an organism work: constant turnover and production of new mature cells from tissue-specific stem cell precursors (as opposed to "pluripotent" stem cells which can in theory produce any cell type, not just a certain tissue).
Neurons, in contrast, are special in that they are not replacable, since a "replacement" neuron would have no way of recreating all the synaptic connections made by the old one. A neuron's connections constitute information storage that would be irrevocably lost if that neuron were to die. Hence, neurons have evolved to spend lots and lots more energy keeping themselves alive compared to a typical cell in a multicellular organism, because the information stored in that neuron is (on average) very valuable to the organism. But life didn't evolve with neurons in mind, and it certainly didn't evolve with 100-year-old metabolically-active cells in mind, so this gets harder and harder as the cells get older, because they are pushing the limits of what cells are capable of.
Neurons, in contrast, are special in that they are not replacable, since a "replacement" neuron would have no way of recreating all the synaptic connections made by the old one. A neuron's connections constitute information storage that would be irrevocably lost if that neuron were to die. Hence, neurons have evolved to spend lots and lots more energy keeping themselves alive compared to a typical cell in a multicellular organism, because the information stored in that neuron is (on average) very valuable to the organism. But life didn't evolve with neurons in mind, and it certainly didn't evolve with 100-year-old metabolically-active cells in mind, so this gets harder and harder as the cells get older, because they are pushing the limits of what cells are capable of.