Consider this:
A. Shopping for other kids' birthday presents is a drag
B. Chances are good, whatever you get them, they've already got it or if they don't it's because they never wanted it in the first place
C. There are a lot more impactful ways to spend money than on yet another Lego set
Someone did consider all these points and came up with a solution, which is to say
A New Way To Do Kids' Birthday Presents
It's called EchoAge and it's kind of like Evite, except they have an option where they can take care of presents too so they collect money from the guests (read: guests' parents). The guest decides how much they want to give and other guests don't see the amount (though you can, as the host). EchoAge then takes a cut, about 5 percent, and divides the remaining money in half. Half goes to the kid to get the present of their dreams and the other half goes to a charity of their choosing.
I love the idea -- though, like the author of the Times piece, don't think I'm quite ready to sign up because of the asking-other-parents-for money deterrent. Pretty fantastic idea, though. I think YOU should do it first and let me know how it goes.