Academia can often be a good place to do that, but it depends on exactly what you are working on. I don't know of anywhere else where I could get paid to work on what I find interesting (but I am not a computer scientist).
One thing you're missing here is the collaborative aspect of academia. Most people work much better when they're constantly in contact with other people who are experts in their areas of interest. In many subjects, you just have to be in an academic environment to get that, since there isn't a culture of online discussion. For example, there is very little high quality discussion of philosophy online. (For whatever reason, the best philosophers just don't engage in it.)
If you're trying to do serious intellectual work, don't kid yourself that you can work out for yourself whether you've got it right or not. You need other experts to tell you when you're full of crap.
One thing you're missing here is the collaborative aspect of academia. Most people work much better when they're constantly in contact with other people who are experts in their areas of interest. In many subjects, you just have to be in an academic environment to get that, since there isn't a culture of online discussion. For example, there is very little high quality discussion of philosophy online. (For whatever reason, the best philosophers just don't engage in it.)
If you're trying to do serious intellectual work, don't kid yourself that you can work out for yourself whether you've got it right or not. You need other experts to tell you when you're full of crap.