Surely by the 24th century, birth control would be 100% reliable? So there would be no more "love children" as such. Unplanned pregnancies would no longer exist.
As said above, love children do still exist, plus if the show were to follow that idea, I always assumed a situation where Beverly slept with Picard and...uh...her husband (forgot his name) shortly after one another, making Wesley's parentage ambiguous.
The bigger problem is that they'd probably learn of Wesley's true parentage as soon as they check his DNA, which they probably do as a standard examination for newborns to see whether anything needs to be repaired or harmful mutations need to be removed or some such.
Was the first season of TNG before parentage tests became a thing?