Sounds a little against the grain but yes, some level of physical attraction is necessary to a relationship. It's pretty much one of the key things distinguishing it from a friendship.
I know people say that the physical side of a relationship is not that important, but honestly it is. I can't beat about the bush there. I mean there is a difference between not finding certain things about your partner attractive, but if you're not able to enjoy a physical relationship due to being completely unattracted to them then the relationship is going to run into some serious emotional problems stemming from the poor physical side. It may not be the most important thing, but it can lead to some very big problems if there is a problem with it. If that makes sense?
I've been in three relationships with men I felt no physical attraction to, to the point where I couldn't bring myself to be physical with them. One of them is now still my best friend, we have such a strong emotional connection. But without the physical connection, it couldn't work. He's my best friend and I love him to bits, but we could never make a relationship work. I ran into the same problems with all three of them, and since they were drastically different people with drastically different sexual needs and desires I am led to believe it was simply the lack of physical connection that caused the problems, since there was no other common factor in the three relationships.
I know people stay in relationships where there is no physical side for many reasons, but the relationship always suffers for it. Even those who stand up and cry out that their relationship is fine, that they don't need to be physical to love someone, they'll then speak on a bad day and it's a different story. It's more than sex, it's the intimacy and physical/emotional connection that is lost that is the problem. If you can't bring yourself to be intimate with your partner in any way because of the level of unattraction, then yes that's a problem.
You ask what do people think they'd do about it. Well, honestly (learning from mistakes!) I would try to be as completely honest with myself as possible. We're never going to be 100% attracted to another person. Our level of attraction towards that person will change over time, it will fluctuate up or down for many reasons in the time we are together. Accepting that is a good first step towards determining how big a problem your lack of attraction is. I'd try to ask myself questions, and answer honestly. What exactly am I not attracted to? Is it just their physical appearence? Or is it their behaviour, their personality, how they treat me? Have any of those things changed recently, e.g. they gained weight or stopped pulling their weight around the house? Has anything changed with ME recently? Am I under stress? Is my libido low in general? Am I unhappy with my own appearence, or my own behavior?
A lot of questions I know, but the point being try to see where exactly the lack of attraction is coming from. I'd also honestly look at how it is affecting the relationship. Am I avoiding sexual contact? Am I avoiding intimacy, likes cuddles and kisses? Does my partner seem aware of or affected by either? How long has it been going on, has it been getting progressively worse or is it a sudden feeling? Do I think it is a problem or am I simply settling into a life with someone I love?
I don't know that any of that rant will help you, just wanted to give you another point of view to ponder. In short, I guess what I'm saying is that it's pretty important to feel attracted to someone on both a physical and emotional level to have a healthy relationship, but it's okay to find them unattractive sometimes, or to always find certain things unattractive. It just depends what all is going on, really.