Can I get an upper lip lift with the incision made along the line of the upper lip?

So why are we not seeing more of upper lip lift with an incision being made along the line of the upper lip instead of under the nose! Most cases of upper lip lift with an incision under the nose are very visible and distort the shape of nose and nostrils but yet it's very rare that I find a doctor that performs the incision on the lip line and wanted to know why is that? Also, are there any advancements with upper lip lift tat don't involve under the nose incision?