Apes/greater monkeys do not smile in the wild. To grin or bare your teeth is a sign of fear or weakness, intimidation.
Only monkeys and apes that have been raised in captivity by humans learn to smile to show happiness or affection, superimposing this biological, instinctive body language from their home society with our own method of communication.
Vegeta smiles only once in canon (if you can even call it that, it still looks like a smirk to me) when ChiChi is so enraged at Goku that she suggests switching husbands with Bulma. Of the two remaining full blooded Saiyan’s (in Z) Vegeta is the one raised between his own race and a warlord.
Does he, like wild apes, hold onto this instinctive, biological imperative to never smile? Is it a sign of weakness in their culture?
Does Goku only grin like a baffoon because he was raised on Earth by humans and adopted their lifestyle and cultural norms?
Goku has a realization that it was him who was the Great ape who attacked the Tenchaichi tournament, where he transformed and destroys the place. Goku finally realizes that he killed Grandpa Gohan when he was little, and apologizes to his grandfather.