First of all, if you look closely along the blade, in sunlight or a clean fluorescent, can you see how much asymmetry is on the edge? Are we talking roughly 60/40 or 90/10 or what?
The basic thing is that asymmetry allows you to reduce your total included angle -- the thickness of the blade just behind the edge -- a little bit, and this means some improved effectiveness in terms of how sharp it will behave. That is, sharpness is all about the meeting of two planes right at the edge, but the thinner the knife is behind the edge the sharper it will seem. (Imagine a really insanely perfect sharp edge ground 60 degrees on a side: the first molecule cuts perfectly, and then the rest of the knife just gets in the way, if you see.)
There are two disadvantages to asymmetry.
The first disadvantage is that if the edge is strongly asymmetrical, honing on a rod -- sharpening steel, whatever -- becomes quite problematic. If the steel in the knife is extremely hard, this is sort of a non-issue anyway, but it's one reason Western chefs do not traditionally go for asymmetry in their knives. I believe the knives you've got are not so ultra-hard that there is any necessary problem with honing, so if you wanted to do that you'd want your edges close to symmetrical.
The second disadvantage is that the knife will have a little bit of "pull" to it in the cut, but unless the knife is quite thick at the shoulder this isn't a dramatic effect. From the way you phrase your question, I presume that you are a lefty and the knives you're dealing with are sharpened somewhat righty, yes? So let me suggest that you try slicing a fat carrot into medium-fat slices. The knives are going to pull a little away from you in the cut, which is going to encourage the carrot to crack near the end of the cut rather than cutting cleanly through. So do you find that this is the case?
I would say that the principal question is whether the asymmetry on these knives interferes with your effective use of them. Ultimately, the knives will work better for you if they are symmetrical or somewhat asymmetrical in your direction, but if the knives aren't working badly for you now you don't need to do anything about it. What you do is, every time you sharpen, grind normally on the left side, then grind another 40-50 strokes; on the right side, grind as little as possible, just enough to flip the burr and get rid of scratches. Over time, the asymmetry will shift over by itself, and there's no reason to pay someone to do it for you. If it is actually interfering, the petty is easy, but switching a whole gyuto -- well, it depends on how confident a sharpener you are, and how much the service is charging to do it for you.
We are talking about roughly a 60/40 asymmetry. I am a lefty - I have rarely (if ever) noticed a problem using either knife. I have a left handed Misono UX10 and I cannot feel much difference in terms of the a "pull" as you described. I like your ideal of having the blade change over time through sharpening. That make practical sense to me.
Yeah, if it's not messing you up and you sharpen your own knives anyway, just let the asymmetry drift by itself and save yourself the money. Don't try to do it all in one go, either: that's actually a lot harder to do well.