There was a small timeframe when Brooks had both the hair and the goatee as Sisko.
Guessing Scott Bakula was the first Captain whose hair was not an issue?
As for Patrick Stewart, neither of the above wigs are what he was going to wear originally, here is a test photo of him in costume as Picard with a wig.
https://images.app.goo.gl/FQjuRj9zAjs2zmJXA
Ew! He actually looks somewhat Shatner-esque in those photos. 
It was my understanding that Roddenberry wanted Picard to be more like Jacques Cousteau than Horatio Hornblower (i.e., an explorer, rather than a military man). Hence the French ethnicity.
I wonder who else they auditioned for the role. I remember Bob Justman saying somewhere that Roddenberry had his heart set on a “hairy Frenchman” instead of a “bald Englishman.”
Then he wouldn’t have had the gravitas a senior officer needs in order to function.