The historical (and continuing--hence the controversial Obamacare mandate) problem is adverse selection. If you know you'll be using a lot of expensive insurance coverage you'll buy insurance--probably the most comprehensive you can get. If you're a 20-something who doesn't think he will ever get sick or injured (or just doesn't think about future events a lot), you may pass on insurance entirely.
Outside of health care specifically, this is also why disability plans tend to be relatively inexpensive for large companies to offer but are pretty pricey--when you can even get them--for individuals.
I'm not sure I follow. Healthcare is mandated, or you'd be paying some penalty on your taxes. So charge a startup fee for some entrance check of taxes, but otherwise why would an individual getting insurance be any riskier than a group? (It does make me start to think of farfetched scenarios like people joining a front-company to get group insurance rates...)
Same with disability, examine the individual coming in to make sure they don't already have a disability that's being covered, but after that why would the individual odds be any different than accepting a whole group? If you do an actual exam, they might actually be better.
The mandate is weak enough that there are still healthy individuals who aren't covered by company plans who are choosing not to buy insurance. [ADDED: And there's a fair bit of concern that the number of these individuals will rise as rates go up, driving further rate increases, in what's often called a "death spiral.]
There are non-employer group plans for certain types of insurance e.g. through something like the IEEE but generally not for healthcare AFAIK.
With respect to disability--leaving aside that an exam won't find all pre-existing conditions such as joint problems--there's still adverse selection. The people who would even apply for disability insurance are a higher risk pool (probably older for one thing) than the working population as a whole or all employees working at a large company.
Outside of health care specifically, this is also why disability plans tend to be relatively inexpensive for large companies to offer but are pretty pricey--when you can even get them--for individuals.