And how much effort does tying up this escort, which you also need to design, build, and crew, babysitting this effectively helpless target tie up, instead of a single ship that can at least shoot back enough to run, thereby getting itself out of trouble, cost?
And you also have to consider the era; this isn't the Picard era, with a literal generation of peace and the Federation as a 300 pound gorilla stabilizing things, this is the wild and wooly pre-Kirk era with the Federation having literally just started out. It's the wild west out there, and going around unarmed, or poorly armed, is asking to get shot. A single torpedo launcher is perfectly reasonable for a ship of this size, role, and era.
Having escort craft which can be used in peacetime as patrol vessels and in wartime as escorts and pickets in fleet actions is a force multiplier for your larger vessels. So the opportunity cost here is nonexistent, because you need that sort of thing already. Why do you think "shooting back enough to run" is actually viable? Unless you're giving these things oversized engines for their cost and role, they're going to be pretty sluggish, and unless you're giving them excessive defenses for their role, they're going to be pretty fragile. Meanwhile, a dedicated escort can actually tie up an enemy attack long enough that your surveyor might actually be able to use its weak noodle nacelles to run away, while also being small enough and well-defended for its size enough that it might survive even that.
You do realize that this weakens your argument even further, right? You already have a good-enough escort ship, build more of them.