Oh, interesting. I always figured that the 737 authothrottle system (actuated differently, as it is) would put the thrust in the right place as quickly by itself. Guess not.
Uplinker is speaking of the 737-3/4/500 - which didn't have FADEC and used a fairly primitive analog electronic engine supervisory control (aka "PMC"). As a result, N1 could vary after speed set (and the autothrottle 'falls asleep' at (IIRC) 60 knots, so it couldn't adjust the thrust levers if N1 started to vary during the TO roll. It's not so much the aircraft as the engine control. At the time the 737-3/4/5 was developed, FADEC was still quite new and novel, and GE was unconvinced that FADEC was worth the trouble (GE wasn't going to do FADEC on the CF6-80C2 until Boeing told them they were not going to put throttle cables in the 747-400 so if they wanted the engine to be offered, they needed to make a FADEC version). As to why they didn't do a proper digital supervisory engine control (as was done on the CF6-80A for the 767) that would have provided proper active N1 control during TO, I don't have a clue.
The 737NG (and of course the MAX) are full FADEC - to set TO thrust it is a simple matter of setting N1 Command to the target - no need to chase N1 as it varies with forward speed. Assuming the engine/FADEC are healthy, they will automatically track commanded N1 as speed and altitude vary.
So in short, Uplinker's complaints about the 737 autothrottle are based on the four decade old version...