Adding go-around thrust without pilot intervention in an aircraft with under-slung engines such as the B737 has terrible potential to take the pilot out of the loop, and the aircraft outside the envelope, in tens of seconds. Alpha floor, in an envelope-protected FBW aircraft, is completely different to that.
As to 'more manual flying training', I'm more concerned that, one assumes, we and our colleagues could all fly a go-around in our PA28s, C152s, etc. But at what point, and why, do some of us cease to be able to carry our that simple manoeuvre in larger aircraft? Is it because the aircraft is too complicated for human pilots below a certain calibre? Is it lack of practice? Is it too much training in OEI operations (far less likely and yet the regulatory requirement for years) and the significant difference in that procedure?
Finally, the common errors in AEO go-arounds are speed exceedences and level busts, both of which are good reasons not to use all the installed thrust for this exercise, most of the time, and metering the right amount is again easiest achieved without automatic assistance, in my experience.
Boeing did not intend the A/T to be used in the way some here are describing, and they've said so. The 737's flight deck is elegantly simple, in functional terms, and there are few things which can be misused. But misusing those few has consequences: I don't believe the guys who designed the CDU meant the scratchpad to be used for noting radio frequencies. So perhaps they didn't foresee the brief disappointment we feel when the aircraft tells us it can't go to 135.375ORTAC.
KISIC.
Keep it simple, intelligent colleagues. Simple doesn't only work for stupid.