Ignorance can be bliss. If you're seriously ill but don't know it, then you have all the bliss that comes with not being ill. The same is true if you're about to get fired but think you're being called in for a promotion. Or if you think you're a charming person but everyone hates you.
And indeed, if you're anything like me, you've once or twice avoided going to the doctors because you don't want to hear bad news. Or you've avoided exposing yourself to tough criticism because you don't want to know if you're doing something wrong. Or you've held a concerning looking letter in your hands a few moments longer than necessary because if you don't open it, it's a bit like there's been no bad news... right?
To will ignorance for the sake of bliss is a common enough thing. But what kind of person would choose that as their default? For most of us, these are some of our more shameful moments. We'd much prefer to be calm and pragmatic in the face of bad news. Why? For the very obvious reason that we have the problem even if we don't know we do, and the best thing to do with a problem is solve it. Simple.
OK, but it's hard to solve problems, and I like bliss.
Ignorance can be bliss, but being completely and desperately stumped on a troubling problem can be bliss. This is why you end up with people who devote their whole lives to science, maths, philosophy and so on--it's not because they're easy.
What makes you happy is reprogrammable. It depends on what ideas you have. So if ignorance can make you happy, and problem solving can make you happy, then there's nothing in it except what's better for you.
I think this would be a nice way to interpret 'the unexamined life is not worth living,' it's not worth living because there's no reason to prefer it to the examined one.