Modern society has the luxury of surplus resources at the moment, and we are able to take care of the old and weak, which we indeed choose to do. If/when that ceases to be the case, the harsh reality will apply to everyone, me included, yes.

Another thing humans are arguably good at is making a longer term plan and investment: if we see that old people simply get shot, we won't be investing surplus value into our retirement funds — at least not of the same sort. Perhaps we'll be building fortresses when younger, accumulating wealth to be able to pay soldiers to protect us etc...

Wait, that's exactly what has happened, except it has evolved into a more systemic solution (our taxes and social contributions pay for police, courts; bigger accumulated wealth allows for more options...).