The most powerful flying control in the 737 is the stabilizer. Why that most powerful control is hidden behind two little switches on the yoke is Boeing’s business, but the fact that it is, has claimed lives (TK1951 et al). Conversely, automating that control in the way the French did, and making it transparent to the crew, is also deadly (AF447).
The stab is sized to cope with the full power go-around under the least favourable circumstances, down to approximately Vref-5 KIAS. Below that speed, control is not assured, and a reduction of thrust is necessary.
Each time I look at the tail I compare the size and range of movement of the elevators, and the size and range of movement of the stab, and remind myself of that.
Regarding the OP’s question: The autothrottle was not designed to ‘wake up’ and provide low speed protection during landing. The fact that it does something reminiscent of the envelope protection of other designs doesn’t make it fit for that purpose, as the manufacturer cautions. I’m not a fan of blind acceptance of manufacturer’s guidance, but in this case, I stick with what Boeing say.