It isn't really a phase issue, but one of polarity.
Some manufacturers, notably JBL, used Minus (Black) forward cone motion, where most of the industry used Plus (Red) forward. This means if you took a small battery and connected the Black to plus, and the Red to minus, the cone moves forward (away) from the magnetic motor.
JBL has stopped doing this with their newer drivers, but most of their previous drivers were like this. One has to verify for sure.
If you get a pair of drivers out of polarity with each other, it kills the bass. One moves forward, the other moves rearward and they cancel each other. This can also occur between two different cabinets. Everything must be checked. Once you've heard it, the sound is obvious.
Gotta love those JBLs.... I've used 'em since the early 1960s. As you point out, the problem is worse with crossovers and compression drives. Harder to tell the movement direction with a HF horn, without a test box.
JBL publishes a spec of which drivers move which direction.
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[="http://www.ofgb.org/reference/Music/JBL/Datasheets/Polarity%20Conventions.pdf"]Link to JBL Polarity Conventions PDF[/]