I didn’t view Watson as taking orders from Sherlock for no reason; maybe I missed something though? Never really about Sherlock and him, it’s the “greater good”. ie, that gif, Watson is pacing but he gets the phone b/c Sherlock is trying to solve a case clue that may help save a victim and doesn’t want to look away/break focus. People matter more than to Watson than his pride, and that’s how canon Watson was. Elementary can’t keep everything because it would be offensive with the genderswap.
Oh, it has nothing to do with Elementary. I don’t compare the two shows; they’re two different incarnations of Holmes and Watson, and are meant to be enjoyed separately.
As for BBC Sherlock‘s John, don’t get me wrong. He is perfectly willing to tell Sherlock off when he’s being an ass, but sometimes he really does just give in on the most ridiculous stuff. Fishing Sherlock’s phone from Sherlock’s own pocket? No, seriously, there was no excuse for that. Sherlock’s hands weren’t busy with anything they couldn’t let go of. It would not have significantly interrupted his activities to reach into his own pocket. But John did it anyway, because…honestly I’m not really sure why. I suppose because it didn’t really cost him anything (except maybe the pride that it’s pointless to cling to around Sherlock anyway ^_^).
Really, sometimes John seems to put up with Sherlock’s crap and obey him on things just because it’s easier than fighting him on stuff. Living with Sherlock is definitely a ‘pick your battles’ kind of scenario. And also, I think, John does it because he adores Sherlock and has a deep and abiding need to be useful. (I really think that the need to be useful is at John’s core, like the need to KNOW and TEST is at Sherlock’s. It’s his inability to do anything useful after being invalided that results in his limp, and it nearly sends him stir-crazy in TGG, till he bursts into the kitchen to ask, “I want to help, how can I help?”)