Of course they would what to procreate, Imagine human sized "avatars," millions of them on earth!? The beautiful luminescent exotic aliens, on earth. In a utopia! What is left to do? Shoop...shoop...aroop...
Look at the erotic fantasy books, they run the entire gamut, from vampires to some crazy aliens engaging in sexual relationships with humans. In fact it would be naive to claim that such things would not happen. It would happen en masse! Like on Risa or that "orgy" planet or sum such.
The amount of information that would need to be transmitted, processed and reintegrated during a single transport of a single human is mind boggling.
So lets see, A 70 kg body would have approximately 7*1027 atoms. That is, 7 followed by 27 zeros.
The transporter moves all these atoms in several second at SUBATOMIC resolution with out so much so as a flinch!
Guess what? To a computer than can keep track of all these atoms in real time, move these atoms 40 000 kilometers away, and reassembly these atom with subatomic precision, genetics would be child's play!
Now combine this with holodeck tech, you would be able to simulate an entire world and all its life, through the planets entire evolutionary history. What would this do to the field of genetics? One would not be limited to a single simulation run, but indeed with a computer system that would be specifically BUILT for these reality emulation runs, there would be no secrets left uncovered, whether it be genetic or any other sceintific discipline.
In fact, starfleet alone, with their subspace FTL computers has the capacity to run a simulation of on entire universe. Millions of these universes. Or did you think project Genesis was just a fluke? Think what kind of massive computational power is needed to encode the genetic sequence of all the life into the Genesis matrix? But, now I am told that some insignificant genetic problem is beyond the federation!? Come on!
As for the star trek writers not knowing the limits or consequences of the technology themselves, well here is my response.
1. Why are the transporters not able to duplicate a biological life form? Fully live ones, or part of them? Imagine if I get my hand blow off, all I have to do is jump into the nearest transporter and presto back as new.
2. Imagine a hot supermodel, her buffer pattern, or what not, is on file, say at the ships computer, what is stopping me from making a thousand fully functional copies of her?

Nothing! Nada! Only the silly restrain of trek writers.
A gram of mass equates to 40 kilotons of TNT. One pound of antimatter has 19 megatons. Do the math. In terms of energy it would not take a lot of antimatter at all to make a new human being! Considering the fact that an average starship burns tons of this stuff per second.
3. The possibilities are endless, with transporters alone. Brain swaps, body swaps, body modification, post humanity anyone? Indeed, one would, and WILL change one body as often as we change our haircut today. On and on.
4. Create life in the holodeck, said life can't leave the holodeck? No problem, beam it out, presto instant body!
Why was the Doctor from Voyager not given a physical flesh and blood body?
Don't get me started on other tech.
Anyway, hope you all get the gist of it...