I think you should trust your eyes. I have the feeling that a real symmetry wouldn't look so good, that you would have to reduce the weight at least a little bit. Still, depending on what spirit of a font you want to create, the perfect symmetry could also create a strange unusual feeling that may lead to something interesting.
I just checked in a Futura book and in the w, the middle stems are not symmetric but the external ones are. To my eyes it looks like the right stem is a bit bolder than the left one.

There are some weird things going on with different cuts of digital Futura available. In Adobe Futura, the 'W' and 'w' look asymmetric in the bolder weights, but inconsistently; just look at the heavy weight, for example.

If a symmetric 'w' doesn't look good, is that because we want it to be asymmetric, or because it appears asymmetric?

I think that a symmetric W, especially the majuscule, may require optical correction because I have noticed that the right-to-left slash sometimes looks heavier than the left-to-right. Oddly I only notice this phenomenon in print, which makes it a PITA to deal with.

I think in the end it's all about how it looks. And you should do it the way you want it to look good, or, better said, the way you think it looks good.
In your example, the left W is humanist in the middle, symmetrical in the "sides", but i think the sides have to looks about the same to obtain balance, where you can "play" in the middle to get the needed optical corrections.
The right W is more of a mistery because the middle is reversed to what it should be (isn't it?). At the same time, it doesn't look horrible, i wouldn't have noticed if we were not talking about that specifically. Also because the right one looks more monolinear.

For your question, i think the problem is more "what does look good?". Sometimes, things that look like mistakes in one letter create good effect in the end (text). Actually your question is a valable one, i just can't find an answer now... I think I can't discuss this theoretically, only with examples.

In my typeface sample I printed out, I do notice that the / diagonal looks the slightest bit heavier than the \ diagonal in the middle parts of 'W', 'w', and capital 'M'. But it's something that doesn't jump out. I wouldn't notice if I weren't looking for it.

To check if this is an optical illusion, I turned the sheet over and looked at the see-through letter shapes. It's hard to tell, but it does seem like I might see the same effect. Since this happens in both the original shape and its mirror image, it sure does look like an optical illusion. It's just a bit baffling, that's all.

Or I could be imagining all this. We are talking about the slightest of effects, after all.

Or is it for optical correction? Are we so accustomed to the humanist axis that given a symmetric ’w’, the right-leaning diagonals will look thicker even though there is no difference in the actual thickness?

I find this to be the case, particularly with a symmetrical A for some reason. I ‘see’ the left stroke as being too heavy relative to the right stroke.

If this is indeed an optical illusion, then perhaps the effect will be the opposite for native readers of, say, Gujarati?

It is even conceivable that maybe only typographically attuned individuals are affected by this.

After working for many hours on an italic font, Romans look back slanted.

**

I don't think the principle of pen-informed contrast will go away, given that readers are habituated to the effect by the predominance of contrasting-stroke type in text.

> After working for many hours on an italic font, Romans look back slanted.

More relevantly:
1) They also look backslanted in a body of Italic (which some typographers do).
2) Semi-serifs look backslanted (which is why Bloemsma put flares in Avance).

> I don't think the principle of pen-informed contrast will go away

1) That's entirely up to us.
2) Actually laymen sometimes complain about the asymmetry in the "A" for example.

hhp