Losing the ability to reproduce was part of the evolutionary path single-celled organisms had to take to become multicellular...
If I understand what you’re getting at then this isn’t a surprising notion, is it? In large multicellular animals, such as humans, only a small percentage of the total cells are proliferative. Tissue turnover is driven by a relatively small number of stem cells and transit amplifying cells that are derived from stem cell division. As it is we can suffer from cancer if a cell escapes the tight controls on its division. Can you imagine the level on control that would be necessary if all of our cells remained proliferative? I can’t imagine that this would be possible.
I was hoping someone would think of the pRb or Retinoblastoma protein or some such.
Regulation of the cell cycle is a very complex subject. For the purposes of this sub-forum and the general knowledge level, I would think that discussion of the specific proteins involved in cell cycle regulation, such as Rb, cyclins, CDKs etc, would be too technical and too much detail.