Most private companies don't offer pensions anymore (for new employees) because companies don't like them. One reason is that pensions incur risk to the employer, while a 401k shifts the risk to the employee.
Until the cash is in the employee’s accounts, the employee is still at risk of not getting paid due to bad investment returns or the employer going under. And it’s not like the pension fund is doing any better than any other index fund the employee can invest in.
Pension plans may not be able to get better returns, but they can specifically balance their assets and liabilities better by picking specific investments and/or buying/operating private companies.
An index fund will underdiversify by only selecting public companies, and over-represent companies with short-term interests (the total opposite of a pension plan!).
The underdiversification or index funds is a particular issue ex-US where stock markets only represent a few sectors.
Pension plans can sure screw up, but they can also be unbeatable.
They all have short term interests, since the people doing the investing aren’t going to be around for the whole ride. In theory, defined benefit pensions are great, but in practice I haven’t seen any evidence that they have sufficiently superior performance to make up for the possibilities of bad investments, corruption, etc.
That is atypical from what I see in the US. In the US, if the pension fund is doing well, that means the politicians offer the government employees unions better benefits, and so all the union members vote for them and since not enough other taxpayers vote against them, we just end up with inflated benefits.
Pensions are a great thing if you work for the same company from 23 (right out of collage) until you retire at 65. How many reading this will work at the same company for 42 years though? For many the company you worked for is no more, others were laid off through no fault of their own. Most of the rest could stay at that first company in theory but there was a better opportunity that you had to not take (even if it turns out worse in hindsight). That doesn't leave very many to make it to retirement working for one company.
Then there is inflation. $5000/month for retirement sounds good now, but will it be when you actually get to retirement?