I'm not saying Root wasn't pretty lucky to get away with that and I know the "close" element of each of those decisions was different, but when an on-field umpire gives a two similarly close (in margin terms) decisions once each way (from a batting/bowling POV, I know both decisions went in England's favour), they're not being "inconsistent" imo. They're simply giving their opinion on impact/hitting etc based on that particular ball, "umpire's call" isn't a thing at that point, it's just yes/no on each factor involved.
Even with exceptionally similar decisions - say for example the Root thing had happened again a ball later but been given, if it was showed to look basically identical on DRS it wouldn't necessarily be fair to describe the umpire as "inconsistent". Impact especially must be pretty tough where fine margins are inovled, as I don't really think a human being can discern the exact fraction of the second contact is first made at, which the techonology can do, so subtle variations in pace/angle of delivery can alter real-time perception enough so that two impacts that the technology shows as identical could legitimately have appeared slightly different on field.
Hmm, now I feel like cnerd, what with all this defending of umpires