That’s strange, since I also took the three wyrm invocation at earlier levels so I could have 4 phrases and that functioned as expected.
Both the Skald and Troubadour subs fit neatly into the ‘infinite spellcasting’ archetype of the Psion multiclass, I’ve found, with the difference being that one increases the amount of resource you have available by making things cost less while the other does it by simply giving you double the amount; two sides of the same coin. Additionally, since skald can only get one phrase per action regardless of how many crits you get with said action (or so I’ve read here) it made sense to me to use Blightheart, which also gives you a phrase per action as long as you’re killing enemies outright or finishing them off and doesn’t rely on multiple layers of RNG.
EDIT: I can still get phrases from melee crits, though.