I find the various uses of the word "privilege" oft-abused these days, and I hesitate to apply such a thing to people to cis because at the end of the day there's nothing they or we can do about the fact that they are statistically more common than we are and that which is rarer is logically and typically not something we make the same provision for as what is average by definition. The whole carving up of society into sections with "privilege" has done little to heal divisions and much more to significantly widen them over the last 15 years, in my opinion. Instead of creating categories of privilege level we should have concentrated on saying things like "we are human too", "we are not all that different from you".
You can't help that you're trans. They can't help that they're cis. We can't help that we are rarer than they are, and most people do not or can not understand what it is to be trans. They do not tend make provision for things they can not or do not understand until they have actually encountered them in a meaningful way in their own lives, and that is the way we all tend to be about most things. And for good reason - efficiency of navigating the world. If you concerned yourself with every section of society's issues that did not involve you, you would have little time left for navigating your own life. We think about what we are concerned about. We don't think much about we are not involved with. Most people are not involved with us.
Different sorts of people face different obstacles in life. If you don't have a heart condition chances are you'll not think about what it would be like to have one. If you don't live in a war zone, chances are you don't think about what it's like to be in one very often. They don't think about what it's like to be trans very often I am sure.
Strictly speaking, this "cis privilege" is the state of going unnoticed and the state of being a part of the average majority. Any outlier is likely to come in for greater notice, and greater disapproval, human (and animal) nature being what it is. It's not just human transgender individuals that face problems. Animals with hormonal aberration and genetic variance of this type also do when they live in social species - there are animals displaying 'transgender' features as well. And we shouldn't forget that animals that have colour aberration like melanistic or albinistic features or other kinds of differences often face problems because they are not immediately recognized by their peers in the wild. I'm afraid I see it less in terms of "privilege" and more in terms of how living things logically tend to categorize their world. Sameness and familiarity is logically of less hazard to them that what is not. That's where the instinct to avoid what is "different" comes from.
Yes, cis people don't have to face our unique problems. And those of us that go unnoticed have less of them.