Not sure what you mean by "should" here, but the IRS definitely considers it to be a gain that you have to pay taxes on, regardless of whether you can sell the shares.
Yes, it's common. They'll say that it's because they don't want unapproved investors on their cap table, which I guess is reasonable, but obviously the main reason is "because they can".
1. You exercise your options, for a paper gain of millions of dollars
2. However, you can't actually sell the shares (there are likely contractual restrictions on selling them, and even if not, there's not a liquid market)
3. So you have to pay millions of dollars of taxes even though your cash flow is zero.
And before you say "but they're ISOs", there's no such thing as ISO's under AMT so it doesn't help at all.