I would assume that, like everything else, the Asari answer to needing more protection than they can muster locally is diplomacy. Make a deal with a bigger neighbor! Promise a portion of the next harvest in exchange for protecting the fields. Sweetheart deals on goods and materials if they include the factories and mines in their patrols. Expert service from professionals in exchange for weapons, armour, ships, and gear. Plus, given the lifespans involved, these deals could have terms lasting decades or centuries before significant payout is expected. Asari bring a whole new meaning to "long term investment".
"How do the asari ever win wars?"
That's the neat part, they don't!
More seriously, the lore is pretty emphatic that, while the centuries of practice and powerful Biotics make Asari strike teams unmatched at what they do, Asari military structure is categorically incapable of engaging in traditional warfare.
... so they built a system where they don't have to. Given the fractured nature of their military, it would follow that any internal threats were similarly fractured. Like for like, no problem. Once they galactic community started forming and they had to deal with different kinds of threats, ones that don't follow the same rules... they called on their new allies in the STG to supply them with intel, so their Huntresses could end the threat early, before anything bigger than a skirmish is a possibility. Diplomacy removes the need for centralized military organization. Which is great and all, until an Outside Context Problem shows up...
Enter the Rachni. Asari strike teams can't fight their way through the hives to assassinate the Queens. Salarian intelligence can't manipulate or isolate weak points. They're forced into large scale warfare, which means they're screwed...
Enter the Krogan. Asari diplomacy (backed by Salarian science) create a new solution, where they get someone else to do the heavy lifting so they don't have to. Which is great and all, until the Krogan figure out that Asari and Salarian forces can't stand up to them in open combat, so they just start taking whatever they want. They're forced into large scale warfare, which means they're screwed...
Enter the Turians. Asari diplomacy (backed by Salarian science) once again creates a new solution so that they don't have to learn how to fight wars themselves. And, learning from their mistakes with the Krogan, they trap the Turians in an authoritative structure, which they are culturally conditioned to obey unquestioningly. Everything's fine and dandy again... sure hope no new Outside Context Problems show u-*REAPER BWAAAAA*
Hyper specialization, it works great until it doesn't. Then you need to get lucky. Which leads to Survivorship Bias, encouraging continued hyper specialization. "It's worked so far, no reason to change", Status Quo Is God.
Plus, it's not like they are COMPLETELY unaware of the problems. Atheyta pointed out the shortcomings, and ways they could shore up their weaknesses. They just "laughed the blue off [her] ass" for it. Why fix what isn't broke? Oh no, the Reapers arrived and reminded us that it IS, in fact, broke! Just like with the Rachni and the Krogan and...
"This is a terrible system" No argument from me on that one. =P