Those theoretical builds are often not very playable, or annoying to play, still using pots, need to have 20 fcr amulet etc.
In terms of damage maybe +20 - 20 monarch is nice, but there are no other stats so you have to overly compensate with fcr, res etc, resulting in not very playable character. Redemption just makes the game so much smoother.
You only need a +15 fcr ammy to hit 125 with a mang song build, because its 30 weapon, 20 arach, 20 rings, 20 magefist, 20 helm (which can be hellwarden). Hence only needing +15 on the ammy.
The biggest difference between the builds is that echoing strikes is consuming a high flat amount of mana drain per second and able to leech it back instantly when hits connect, fire warlocks spike down and then back up again after a delay because of the gigantic cost of apocalypse and then simultaneous deaths when the siphon kills kick in, and blood boil costs much less mana and has much higher maek so in gameplay you're basically glued to 95-100% orb capacity.