"Important money", such as retirement savings, should definitely be indexed in low cost funds, held for decades, and not traded. If you don't know the overwhelming evidence for this advice, read the many books by the late, great, Jack Bogle.
Some small amount of residual funds could be used for "trading for entertainment", going to Las Vegas, etc. Don't expect to "win", but maybe you can learn enough to "stay at the table".
Successful proprietary trading firms seem more akin to market makers, 50+ employees, perhaps have exchange memberships, expensive infrastructure, large well-maintained databases, etc, etc. -- I don't see how an individual could compete with that. Plus, you can probably only learn their "edge(s)" by going to work for them.
Not what you were looking for, but my two cents.
Thanks for your view on the market and trading in general.
Despite the fact that I hate to admit it I must agree on your conclusions. Both regarding the Index approach but also regarding the market edge. Trying to "beat the market" or even make money in the market by actively trading seems difficult to be honest. It bothers me in the sense that I've spent/invested a huge amount of time in the trading just to come to the bitter conclusion and (perhaps) giving it all up. At least when it comes to actively trading. The randomness is simply too large of a component and playing the game with "randomized chess board" is simply too difficult.
I'll most likely give pair-trading the last chance. Alternatively, building the shovels rather than using them is another approach which I might give a chance as well.