So, we will see if this privatization of pensions really benefits us all or merely enriched a generation of asset managers while absolving the corporate and the government from providing pensions for workers.
Other options included pensioners taking a haircut and/or workers taking a paycut, neither of which is particularly palatable and still runs us into the ground eventually. Increasing corporate taxes could square the circle for a little while, but then corporations would slowly move more operations offshore, decreasing tax revenues eventually anyway. There's also the option of cutting other government expenditures, but eventually that stops working and at least some of the things that were cut can't stay un(der)funded forever.
The only other (distantly) feasible idea I can think of would be, again with an eye to Japan (of the past), near-total isolation from other countries economically, but that would have an even more substantial stagnating effect.
How does this jibe with ever-increasing profits?
A traditional pension fund cannot afford that kind of risk without a massive cash buffer and could not have captured that value anyway because it cannot cover its own firm's losses with some other firm's gains. After all, it's not like the same 500 companies are occupying the index as decades ago, and even those that stick there have changed relative positions a lot.
The only thing that could have conceivably replaced traditional pensions and captured all of this value and given it to the workers "fairly" without suppressing the factors that made it possible would have been a sovereign wealth fund run passively but competently by the government, but such a thing is in and of itself a moonshot.
I think it's more than "a few". For one thing, many 401k-equivalent funds that government employees can make contributions to are low cost index funds, and there are lots of government employees. For another thing, most 401ks offered by large corporations also offer low cost index funds, which many employees contribute to because they're usually the default that you get if you don't pick something else, and there are lots of employees of large corporations.
Nothing can protect you from ill timed trades.
However, trades can only be ill timed if they are made. If you just pick an index fund with an appropriate time horizon for your planned retirement and then leave it alone, you don't have to worry about ill timed trades because you aren't making any trades at all.