Unemployment isn't a stable situation - even if you're doing OK today, the slightest problem can drop you off a cliff.
First, you no longer have Short and Long-term Disability Insurance. That's the one that kicks in and pays a significant portion of your regular paycheck if you're unable to work - say, because of a broken leg. It's virtually impossible to get if your income is coming from unemployment insurance, consulting, freelancing, or any other non-traditional source.
Once when I was freelancing, I went roller-blading with my daughter. After doing a knee-plant that - without pads - would have put my knee cap somewhere behind my ears; I told my wife, "I have Life Insurance but not Disability so if I fall, just shoot me."
Second, any major expense - even a bad car repair bill - can flatten you. The most dangerous are medical bills - you don't get a choice when they appear and, unless you're still on COBRA, you probably have lousy insurance that won't cover them sufficiently.
Another big reason to get a 'real' job with real insurance.