I think the OP knows that her disagreeing with this is not attractive and that is why she has come here to talk about her annoyance anonymously.
But I don't blame her! I understand the annoyance. There are lots of different ways to slice it and they are all really hard to object to in public.
I can't bear people like this. I share a birthday with an acquaintance, we were both on maternity leave at the same time. At my extremely modestly festive baby-filled birthday lunch, at my house, which I arranged for "us" as her birthday was on the same day, she spent a large part of it in the garden arguing with and about a couple who had pulled out of some posh restaurant dinner she had planned for herself and her"real friends". She was furious that they said they "couldn't afford it" because she knew what they earnt and what their mortgage was! The arrogance was astonishing. I thought it was incredibly insensitive that she was making her drama about this such a big focus of the lunch which was my only birthday celebration and clearly didn't count. And I could understand that you would be hurt that people pulled out of something on the day, but couldn't believe that she was so comfortable sharing all this and making this drama so public and that she honestly felt justified in being annoyed. Hurt yes - annoyed, oh do fuck off. Going on about all fucking lunch? Shut the fuck up.
Anyway if I had said any of this I would have been the bad guy so I am ranting at you instead, 4 years later 
And I totally get where the OP is coming from here. Everyone gets a birthday. No one can go away for 6 birthdays in one year at £1k a pop. So by proposing this, the OP's friend is implicitly elevating her birthday to higher status than everyone else's. She is obviously comfortable sending the message "my birthday is the most important" (which blows my mind) and if she was challenged on this would say "I didn't mean that, because you can do what you want for your birthday" without having the good sense to see that, no they can't, not after she has done this and used up the friends money, annual leave and family time on her birthday.
Of course you can't say any of this. Of course you can only go or not go. But I don't blame you for being annoyed. What you are annoyed about is something unmentionable - the knack some people have about making themselves top priority, and the cheek they have about their stuff being so special and important that is unreciprocated with your stuff.
Don't like people like that. Don't want to see people like that any more. Too tired.