There's a difference between a plan someone worked and paid into and one where you never have to work and get to free ride on someone who does

But yes National pensions can have the same problem, as is currently the case in France. The elderly vote themselves higher and benefits, waiting to back breaking taxes on the diminishing number of middle-aged workers

Pension systems don't have a huge effect on the incentive to work. They have some effect but not enough to collapse the system. But we could possibly see a collapse in the future in a country like Italy.

By the way, I support some level of rich-to-poor redistribution, not sure what's the optimal level but to get a reasonable range of where the optimum could be, look at the top 20 countries.