Who are built from the ground up to do nothing but fight and kill using weapons.
Starfleet is a scientific and humanitrian organisation.
Show me one advanced science lab in a battleship, or astrometric studies, or advanced studies of say cancer research, medicine, cosmology, cybernetics.
I'll wait here until you post one.
Not quite what you were after, but
here you go.
A few points from it:
Code 6100 - Chemistry Division
Code 6900 - Center for Biomolecular Science and Engineering
Code 7100 - Acoustics Division
Code 7300 - Oceanography Division
Code 7400 - Marine Geosciences Division
Code 7500 - Marine Meteorology Division
Code 7600 - Space Science Division
They don't put that stuff on a
battleship because the
battleship isn't designed for anything except
battle. Hence the (outdated) term
battleship. But the Navy, who according to you is built "from the ground up to do nothing but fight and kill using weapons" does tons of research in multiple different sciences. The same goes for most of the other services.
And if they did join forces with an organization like NASA, and if they did build deep space vehicles, and if those vehicles were heavily armed and armored (as every single one in Star Trek is; even Crusher's medical frigate had weapons and shields), you would
hope that they'd have some military forces onboard, too. Else that would just be incredibly irresponsible given the weapons of mass destruction they have at their command. It'd be like giving Doctors Without Borders tactical nukes "for defensive purposes, of course."