I do opine, OTOH, that the claim of flying accurate speed under UAS using a GS readout is bogus. The present procedures - which do not include any GS at all - give good enough result within 10 knots already as they are.
I'll weigh back in here. I don't think anybody is claiming that GS will give you an "accurate" speed, depending on how it is defined. But what stands out like dog's balls to me is that if GPS GS was used in these two scenarios, the speed could have been actively controlled/limited to enable continual overriding of the MCAS at a mid-speed instead of Vmo.
From an old 737 FCOM, the 70 tonne flap Up holding power is only 66% N1. The UAS is what, 75%? Even with a slight climb (UAS Memory Items) the speed is going to start increasing, and as the speed increases, the drag reduces and the acceleration increases. The Ethiopians were dead in 5 minutes, commencing the last dive at Vmo. Do you lot really think that, with all that was going on, pulling out the QRH and going through the tables while maintaining the UAS memory Items was actually going to work? The Lion Air guys had the QRH out, apparently. They were flying for 11 minutes and still dived into the ocean at warp speed. The GPS GS would have told them all they needed to know about the speed. Ignore it at your peril.