Personally I'm fine with that since my end goal in life is not about bending over for others to gain advantages or avoid disadvantages.
I never use Web cam at work for example. I'm usually the only person not on camera in phone conferences. I'm sure it's a disadvantage but I'm somehow still doing fine. :)
If you are unique, sure, you can have an extravagant and highly exotic CV. It is not the reality of many people, especially when someone needs to ask whether they should put a picture or not.
I also am often reading CVs and they never have a picture. Most of them don't even have a name, just initials.
I think I never saw a CV without a name, and rarely one without a photo. This is in high tech.
That way we make our choice based only on the person's experiences (thi also prevents us from contracting this person directly, which is fair game I think).
The only time we see names is if the person does not come from a recruiting company, and even then there are not pictures.
As a matter of fact, photos are getting less and less common on CV's in France.
As for the photos, i am not sure how many CVs you see, but the ~100-200 I saw in tech across the last 5 years all had a picture (except a very few ones, which I noticed). I do not pay much attention to the picture because of experience (I am horribly bad on pictures, and some of the best people I worked with were extravagant), but this is me.
There is nothing legal or illegal there, just a matter of tradition and therefore not having one makes you stad out, not necessarily in a good way.
Except when they are the standard in a culture other than yours. A CV without a picture in France is a bit suspect and it will leave the feeling of something incomplete.
When you search for "photo cv" in French, you will see a lot of sites that start with claiming that the photo is not compulsory, cannot be required and that the lack of a photo cannot be a reason not to assess your CV. Just this shows that the reality is that it is expected.
A lot of discussions is around discrimination. If your name sounds [put your most feared origin here], you can hide the picture as much as possible but this will not make a 12th generation Brittany-ion (no idea how someone from the Brittany region is called).
Then there is the address which also reveals a lot and at the end of the day the fact that you did not put a picture is likely to be against you.