Our resident celebrity might feel differently about this, but the one celebrity I know takes great pains to make himself unreachable, personally. He is VERY busy, tho, so, what little free time he does get, he wants to be able to spend with family and friends or song writing.
Point being, I would be surprised if someone who has a couple million plus Twitter followers is going to have an email address on their website, at least not checked by them, personally. The only exception that comes to mind was Bruce Campbell, back in the pre-Twitter days when he was more hands-on with his own website.
Actually I generally only come out of the broom closet for specific, small communities. I don't have a publicly available email address, I don't have contact information on my website and (shhhhhhhhhhh) I don't handle my FB page, someone else does.
The reason for this is simple: despite having an FAQ up, no one (or at least, not one of the people who should) ever seems to read it. Now, I can answer the 5000000000000000000000000000000000000 iteration of "Are Companions really angels?" or I can actually write something. You know, stuff I am paid to write. So I can pay bills.
Within the small communities where I do operate openly, I know that you folks are
mostly not too stupid to read the FAQ going to invite me into discussions of things that are interesting.
That will be the case with the vast majority of celebrity types. It's not that they don't
want to, it's that the clueless wonders would devour every spare nanosecond of their time.
However if you are demonstrably clever enough to find the work around, most of the celebs I know are at least gracious enough to get you some kind of answer.