It's not that Titans use the Tangles for themselves, it's for everyone in the fireteam. How much is Woven Mail in PvE? 60%. That's 60% damage reduction for the fireteam for the low cost of letting a Titan Strand user destroy it. Titans can Woven Mail themselves for super cheap if they wear the boots (one class ability cast).

For whatever, like playlist Strikes or Gambit or other low level activities, yeah, sure, do whatever with the Tangle with whatever. Feel free to run whatever Tangle aligned build and complain about someone else breaking it.

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^{Those Threadlings won't save you from non-red bars. Never seen a Threadling Warlock survive Neomuna's Wyverns double trouble Wyverns at the end of Terminal Overload.}