Let's talk about Jean-Luc and Beverly.
Jean-Luc Picard was born in 2305. Beverly Crusher, nee Howard, was born in 2324, making him, as you say, 19 years old at the time of her birth.
Beverly met Jack Crusher some time after being admitted to Starfleet Academy in 2342 at the age of 18. We do not know exactly when they met or for how long they dated, but they married in 2348, when she was 24. Wesley was born a year later. According to Memory Alpha, some time after their marriage, Jack served aboard the USS Stargazer under Jean-Luc, and Jean-Luc met and fell in love with Beverly. Jack died as a Stargazer officer in 2353, when Beverly was 29 and Jean-Luc was 48.
So, let's assume, for the sake of this argument, that Jack and Beverly met Jean-Luc in 2350, giving them three years to build a meaningful friendship and Jean-Luc three years to fall into unrequited love with Beverly. Jean-Luc would have been 45-48, and Beverly would have been 26-29.
The 40-something Jean-Luc never pursued a relationship with the 20-something Beverly.
I repeat: The 40-something Jean-Luc never pursued a relationship with the 20-something Beverly.
When they met again in 2364 aboard the Enterprise-D, Beverly was now 40 years old and Picard was 59. Over the course of TNG and the TNG films, they went from ages 40-55 and ages 59-74, respectively.
There is a world of difference between a person in their mid-to-late 40s pursuing a person in their mid-to-late20s, and a person in their early 60s pursuing a person in their 40s, or a person in their 70s pursuing a person in their 50s. There is even, I would argue, a significant difference between a person in their 40s pursuing a person in their mid-20s vs. pursuing a person in their late teens or early 20s.
The basic issue here is power differential that is unavoidable in an adult who has gained major life experience vs. an adult who has not gained major life experience. There are two basic ways to think about it: The attainment of a certain level of personal autonomy by one's mid-20s, and the difference in ages expressed as a percentage of the younger person's age.
So, if a 30-year-old is chasing an 18-year-old, that 12-year age gap is two-thirds of the younger person's entire existence. If a 52-year-old is chasing a 40-year-old, then the age gap is less than one-third of the younger person's lifespan. If a 74-year-old is chasing a 55-year-old, then the age gap is only 21.8% of the younger person's lifespan.
To put it another way: The age gap matters less and less as the younger person ages and thereby gains more personal autonomy, self-assurance, and self-empowerment. The power differential lessens meaningfully.
Anyway.
Bottom line is that a 30-year-old Picard wouldn't chase a 19-year-old. The 45-year-old Picard didn't chase the 26-year-old Beverly in spite of his own feelings, and the 60-something Picard was extremely reluctant to get into a relationship with the 40-something Beverly during their time together aboard the Enterprise.
Picard is an ethical guy, and he wouldn't chase a kid.
In my example, the three I know of were chasing him.
One was sort of flirted at by him, but that did t work out.