One very important part of this discussion that seems missing so far is this.
The thottle = speed dictum is related mostly to jets...particularly heavy jets. This is because they have such relatively high weight and therefore momentum that if you're slow and lower the nose you will just get a huge increase in ROD...long before you get any meaningfull increase in speed. It's fairly similar in very heavy prop aeroplanes too...but mostly jets...with prop aeroplanes, particularly big multi engined ones an increase in power brings about an increase in lift from the accelerated air travelling over the wings and then some acceleration....pour on the coals in a jet and the lift only increases as a buy product of the extra speed....jets are usually approaching to land on the back side of the drag curve which just exacerbates the effect...prop aircraft, particularly little ones are not...to anywhere near the same extent anyway.
So in a jet we trim for a specific attitude and hold speed constant with thrust....a little slow=more thrust...a little fast = less thrust...a little high = lower the nose...a little low = raise it. The very high momentum means that raising or lowering the nose has little effect on speed in the short term. In a jet if I am a little low and increase thrust I'll just go lower faster because I don't have the instant increase in lift you get from increasing power in a typical GA twin/single.
So many techniques filter down to GA from Airlines and are assumed to be better simply because that's the way the big boys do it.
That is just plane wrong...I don't fly my Bonanza the same way I fly the 767 I earn a living in...they are very different aircraft and require a slighty different technique.
In a light aircraft Power and Attitude = Performance....so too in a heavy jet....just the technique used to arrive at the required performance varies slightly.