Auto-Motor-und-Sport has an article that quotes Toto Wolff saying that they changed Hamiltons strategy because they feared he would have a difficult time maintaining pace with his softs to the end of the race. E.g.: become a sitting duck, compared to Rosberg on fresh SS.
I still feel this is utter rubbish what Toto is saying here:
Link Austrian lap time history chart / FIA Event & Timing Austria 2016 GP
Up until Lap 54, Rosberg on 11 laps older tires was still doing consistent 1:09 times.
Lap 53:
ROS: 1:09.3 (43 laps old S)
HAM: 1:09.1 (32 laps old S)
Therefore, it was safe to assume that Hamilton could continue to maintain a similar lap delta up to at least lap 54+11 = 65. That would mean there would still be 6-7 laps to cover till the end.
Assuming Rosberg would be 1 second quicker on new tires (he wasn't), he would still need to cover a gap of at least 22 seconds, the duration of a pitstop, and overtake Verstappen to gain on Hamilton in that time. That would mean by the end of lap 65, there would still be a gap of at least 11 seconds remaining, assuming he'd be the 1 second quicker, that he would then need to close in 6-7 laps. That IMO is a very substantial gap, unlikely to be closed, especially assuming Hamilton could have backed off. The history shows us that both Mercedes, after pitting on lap 54/55 did slightly better/lower 1:09 times. Even Verstappen, who stayed on his 1-stop, was able to continue to do 1:09 times till the end of the GP.
I would have preferred to see Mercedes pit Rosberg and then re-evaluate Hamiltons strategy on a lap-to-lap basis. Seeing Rosberg pace and informing him if things didn't look good. At least they gave him the opportunity to undercut, though on the harder compound tire and the slow pit, it just didn't work out.