I agree there are probably a lot of people who need a licence and are just avoiding it. But filling in a form to say you don't need it won't help fix that issue. They would simply fill in the form and lie on it. The BBC would be no nearer to proving they need a licence.
But there is no legal requirement to fill in the form declaring you don't need a licence. If I stopped needing a licence I would probably fill it in the first time to avoid the hassle, but then ignore it at "renewal" time. There is no reason to fill in the form other than to stop a few letters being sent to you, which you can simply ignore.
I'm afraid I'm in the camp of wanting the BBC to move to a subscription service. Several other services offer me real value so I pay for them. I barely watch anything on live TV because I find most of it rubbish now. I would happily stop watching if I could save the money instead. The world has changed and TV is a very different place compared to when the licence fee was started.