Caller's Doublet is inferior to everything. Convoker's beats the damage, Hagondes(pref)/Glyphic for perp, Anhur for skill.
There's really no reason to have a Caller's Doublet if you have all of those, and they're all relatively easy to obtain (Anhur being luck/money cost).
The only situation that might arise is if you think the 10 summoning skill is better than the 2% BP damage off Convoker's, but that's just preference. The majority of the time Summoners are not fighting content that requires large amounts of accuracy due to how weak we are in a party, so generally the damage will win anyways. If you're really worried, just stick it in your accuracy set and there you go, if you ever actually do need it, it will be there.
Incorrect.
Caller's outperforms Convoker's constantly. (+2v+1)
Because it's the same thing as having nothing but MAB in a nuke set: sure you might hit for slightly more, (that 2% translates to verly little more damage. 2~300 at most) but you're gonna get constantly resisted making your DPS crap.
Barely less damag all the time >>>>>>>>>>>>>>> big damage rarely.
It's the same reason why Caller's Bracers +2 were 1000000x inferior to Summoner's +2 even when the set bonus was taken into account.
And maybe you're weak in a PT... But I know how to do things in PT for content that matters: eg Delve 2 and whatnot.
SMN has become FAR better than it used to be in terms of DD.
And even in WKRs can you tell the difference between how bad Convoker's is... The SMNs who have BPs go all over the place in dmg? Convoker's.
So it's not just "things that matter" where Caller's is better, it's any iLv content.
As for Hagondes.
No.
MAB will never beat out +10% hard damage. You'd need to have something like +100 or more for MAB to perform better.
And Hagondes can't get that much MAB by itself.