I come off as angry here more than I intend. I definitely wasn't here, so I apologize for that. I won't flame you though. Just because I believe someone is wrong about a topic doesn't mean I look down on them in general (those feelings are reserved for cheaters and people who join games just to ruin them...as in ruining them is their express purpose).
Nor in youtube when you said you can queue them for failgold? Just want to get on the same page here and not misunderstand your point, nor anger you again.
Well, if you got failgold you didn't build them. You "attempted" to build them. The problem with doing this is the unreliability. As you noticed, sometimes it takes forever when what you need is gold or gold stores now.
Well that's why you're a deity and I'm a mere mortal monarch practicing blasphemy on a daily basis. Prometheus gets his liver eaten out just for showing me how to make fire.
I practice blasphemy a little too much too. I'm just abusive

.
But seriously, the outcome of a HA or cata war is going 1 of 2 ways:
1. You successfully roll the target(s) and are likely to have unlocked heroic epic to bolster an already strong standing army. In this case, you need money/research, not more production.
2. Your rush sputters out, and you're left scrambling for units. Capturing and holding mids in this scenario isn't likely. You also have to weight the extra

with the less

you have as war weariness is not harsh earlygame...a 25% boost when your 2 best cities can work 2 less mines than under rep/monarchy isn't very helpful.
There are exceptions to this rush scenario (you rush and take a city the AI happened to put up pre-1000 BC mids on your border, and have a ton of

resources), but those definitely qualify as "fringe", especially since a very powerful

start doesn't beg a player to rush.
A lot of players on these boards just don't realize what is possible. For example,
if you avoid researching/trading for fishing, you can have trebuchets, xbows, and pikes by around 500 BC. Are pyramids more valuable than that? Even on deity pre-1200 AD rifles aren't super common. How long would it take for monarch AI to get a tech to stop you? Players should consider this before investing heavily in other things. This game is all about tradeoffs.
Alternatively one can start isolated but bulb astro by late BC/early AD. Or very early lib.
When HA rushing, shut your slider off while building them, and store lots of money. Store even more as you conquer cities, and you should have enough time to capture a LOT of cities, extort tech, mass build research, etc before you run out of time and strike. In my challenger V let's play that had monarch/domination, I was running close to -200

/turn at one point in the game, but never lost a unit to strike

.