Broodweaver is the only Strand subclass lacking an aspect or exotic that grants Woven Mail.
Weavewalk - being the aspect intended for survivability - is the best fit for this.
It is currently vastly underperforming, as is the Broodweaver generally compared to the other Strand subclasses. I don't care for the excessive damage reduction it grants and would immediately trade a chunk of DR for more active survivability in the form of 10 seconds of Woven Mail upon exiting Weavewalk.
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I agree that Weavewalk needs to offer something else, if it is going to remain a 1-Slot Aspect. I think it would need to be stricter than simply entering and exiting it to grant Woven Mail, though; it would generate a lot of complaints in PvP that you could get Woven Mail for a quarter of a melee charge and effectively have it for every fight. Needing to expend a full charge would work, and I don't think it's unreasonable in PvE given Monte Carlo, Pugilist and Thread of Fury.