Batting average treats a home run and an infield single the same, but plenty of people use it.
ERA also gives the same credit for the runners the pitcher allows to score and the inherited runners that score on the following reliever. ERA is also more influenced by ballpark than WHIP.
ERA has the advantage of being more popular and more recognizable, but for relievers it gets easily blown up by one bad inning. If an RP throws 60 IP per year, every earned run is worth 0.15 on his ERA. So one 4 ER inning can make a substantial difference, and your season long 2.40 is now 3.00.
Also what about all those unearned runs? Why do they get completely ignored? If the team behind a reliever plays great defense, the pitcher benefits. But if they play poor defense, no impact at all? It just gets ignored? Like it never happened? Even if the reliever pitches like complete s*** after the error?