Do losers average losers?
Averaging down is usually compounding your loss had been my experience.

Or, throwing good money after bad money.

Averaging in or out looks a lot like hedging/scalping the gamma of an options position. Counter trend if you’re short, trend following if your long.

How you amend your position with respect to some factor (be it equity, time, what-have-you) is imho the next frontier, and the most productive, to-date, endeavor in portfolio management (and little understood because people had not crafted the tools to study it).
Adding to losing positions is portfolio insurance in reverse. The points bad of portfolio insurance, are points good now in this exercise and vice versa. There is an enormous, fertile, ocean-sized domain to be explored and exploited here, and there is the opportunity to step beyond mere aphorisms in this regard.
Ralph, as I understand what he does is the worlds master of averaging positions—but not for short term trades—only trades where he knows the position will show a profit…unlike we short term traders that often buy at all time highs, etc.

Just because a trade goes against you initially, doesn’t mean the trade isn’t good. If the conditions that got me into the trade in the first place still exist and I didn’t go all in with my full package initially, I’ll add to my position. All it means is I was a little early on my initial execution, and when the trade is working, I’ll add aggressively.

Yes indeed.

And so I found myself in a hotel room, in November, in Boston, staring at the face of a large margin call, literally seeing stars, that had to be met in a few hours to stay in the game.
With the great Mike Epstein ad my confessor on the phone, I boarded the T in Cambridge to deliver the check downtown and met the call.
It was a defining morning for me. 

There is always a bit of truth to an aphorism.
For example: The early bird catches the worm.

Rocky, yes, exactly. As a general rule,  averaging down, say, is a good way to get quite buried. What you say about carry, noise, etc. all certainly apply as well as far as I can tell. It IS complicated, hence the reason some sort of framework is required to arrive at conclusions to go about capitalizing on the idea (or, seeking to capitalize on other criteria)
Let’s wind the clocks back to early 1987. At that time, there were certain programs pitched that were essentially based on portfolio insurance with a delta calculated assuming a strike at the current index price (in effect, the opposite of an “averaging down”-type of strategy). What was not widely-known of such strategies, is that losses incurred would take extremely long to recoup. The very programs pitched as ideal for retirement accounts, clearly were anything but (i.e. they were not crafted with an eye towards being at equity highs at some specified future point in time).
On he contrary, to be delta=1, 100% invested, is to be at very close to the full-out expected (asymptotic) growth optimal fraction, and endure all the lovely barbs and buds that has to offer — but who is operating based on this? Clearly there are benefits (early-get worm!) but there is far more to it than the aphorism suggests, and I think there is a lot of low-hanging fruit to be had here but, as you point out, many real and serious considerations.