All else being equal, in the dry more rubber on the road means more grip, whether its the result of a wider tyre, a slick or competition tyre that has a tread pattern with more "land", or a bald tyre.
But there are reasons why bald tyres might not have more grip. Old tyres have less grip than fresh ones, and the sort of people who drive around on bald tyres are often running very old tyres. There are two reasons they have less grip. One is the gradual hardening of the rubber compound over time as the components in the rubber that keep it soft eveaporate out. And the other is that as the tyre is thermally cycled - heated and cooled over and over again - it changes chemically and goes harder. As well the tread rubber is designed for grip whereas the rubber used in the carcass of the tyre isn't, so if you've worn it right down to the carcass, well, who knows.
There is also the effect of temperature. A deep tread pattern generates heat through squirming of the tread blocks that may overheat the tyre and reduce its grip. A very thin tyre on the other hand can have the same problem because it has very little mass to absorb any heat, so it will both heat up quickly and overheat quickly.
The result is that in classes that require road-type tyres what competitors do to maximise their grip and stay legal is to buy as fresh as possible tyres, then shave the tread down to a minimum they are allowed to. And with slicks the best grip is obtained with a tyre that's only been used long enough to take the "green" off - the slick shiny surface they come out of the moulding machine with.