It's not a matter of increasing your recharge with 4 pips, it's that your shields gain 60%~ strength by putting 4 pips in them. Your 1000 shield Anaconda suddenly becomes 1600 shields. It's a big difference, and power management isn't as simple as Engines to get on target, Weps to fire. For example, if you're flying a mixed loadout ship with say, beams and MCs, and you're fighting a Python; you want to drop the Python's shields pretty quickly, so keep 4 in Weps to melt his shields at the start of the fight while yours are still intact. Transfer to Eng as necessary to keep him in your sights, and once his shields drop (he's obviously still shooting you) so now transition power to your shields. Your MCs don't use hardly any energy at all, so now you've added 60% or whatever to your remaining shields, and can burn down the target at your leisure.
Now what if the Python is melting your shields faster than you're melting his? That's when you stuff 4 pips in shields, burn whatever Eng charge you have as boost to try to dodge for a few precious seconds while you spool up an SCB and kick off a heatsink. The extra pips in shields will help them last just long enough for the SCB to fire off, allow you to avoid the terrifying prospect of continuing the fight sans shields.
Basically what I'm saying is combat is/was a lot more dynamic than just "Transfer emergency power to phasers" and no one solution fits everything. I've had fights where it was in my best interest to keep firing as long as possible, and some fights that relied on simply not getting hit at all, so more power to engines was preferable. Try to read your opponent and see what is appropriate.
