Axe garrisons are sufficient to keep the power rating at 0.7-1.0 on monarch which is plenty to ward off all but the most Monty neighbors, and plenty to defend if it comes to that.
I am not interested in conquest, if i was then i would be using warriors or archers. This is a peaceful way of keeping your empire happy while at the same time diverting resources to defense without specifically having to think about it or MM it to any degree.
If your intent is to stop yourself once they decide to declare, you just need enough forces to match their invasion stack. This is attained vs everyone but toku by camping a unit in their territory near their stack (which is always flagrantly obvious), and making sure you have enough forces to match on defense(the AI are so brilliant, aren't they).
If you're trying to prevent a declaration at all, having "sufficient" power rating is a garbage argument for axes. There are very, very few AIs that will not declare at a 1.0 power ratio with you. If you're below that, forget it completely. For the people with low peaceweights, they can decided to declare on you when you are markedly stronger
Let me build on this with some basic war powers: Shaka's will declare max war on you with 90% of your power. Ragnar/nap need to be a little stronger (1.1/1.2x). Bismark? Brennus? Darius? Hannibal? All 1.0. There are some surprises - churchill and washington are the same as shaka (though they'll hurt less). Even peaceniks like pericles, liz, lincoln, and hatty will declare at .9 of your power!!
What sets some of those guys apart is their war chances at differing dispositions. Shaka is 40% at cautious, sitting bull is a whopping 90. However, now you're relying on dice rolls and diplo, not power!
You're telling me that monarch + you think it's a good idea to keep enough power to deter a DoW? Look, I AM a warmonger, and I'm telling you that sufficient power to AVOID war entirely is IMPOSSIBLE with the AI bonuses, ESPECIALLY if you are a builder. It is also unnecessary - if you're using axes to grow your cities to huge pops early on, you're overbuilding military. How many axes vs warriors until you could have had libraries, courthouses, and other improvements instead? With the same functional odds of war and the same ability to repel invasions? You have a substantial opportunity cost to your tech rate by not building cheaper garrison units. You'll reach key techs more slowly.
In summary: If you aren't attacking them, it's foolish to sink hammers into such units. They won't be well promoted to justify upgrades, they won't be necessary for defense (and it'll cut into your happiness if you use them for that purpose), and they sure as hell aren't going to prevent war.
So, what's the upside then, assuming VS the AI? The equation changes a bit versus humans, but it's pretty bad to call oneself a "builder" when playing against humans in the mindset of attacking you to begin with, so I'm going to assume you're talking about taking on the AI, in which cases using axes for anything but rushing or anti-rush on the borders is pretty suboptimal.