So it would appear that the inlet duct of a turbofan engine works a lot of magic in reducing shock losses, namely by slowing the flow to subsonic speeds?
The inlet doesn't slow the flow to subsonic speeds because the flight velocity is subsonic to start with.
Incidentally, the inlet doesn't determine the speed of the air at the engine face. The engine takes what it needs and slows down or speeds up the air as appropriate for a given thrust setting and flight velocity.
Shock losses are caused by the fan design, ie tip speed, and reduced by the fan design, ie thin blade sections and profiles to control the diffusion to subsonic speeds within the blade passages.
why can't we use an existing turbofan design and just have all the air exiting the combustion core drive a conventional (ducted) fan?
What is the reason for a propfan or UDF?
It's to allow flight speeds of about Mach 0.8 with better SFC than today.
These concepts attack the propulsive efficiency part of the SFC.
This has been done continually since the advent of the turbojet by increasing BPR until today the ever increasing weight and drag of the big fan engines intake and cowling are negating the benefits of jet speed reduction.
That's why you don't want a ducted fan.
Since propeller efficiency is very good due to its high BPR up to about M0.65 the focus is on how to redesign the prop for M0.8 with low compressibility losses and much higher power loading (because you have to go faster). The first requirement leads to thin, swept blades, and the second means maybe twice as many blades of smaller dia and spinning faster (which reduces the reduction gearbox size at the prop moves towards the power turbine speed).
This achieves the goal stated above.
The propfan is a turboprop with an advanced propeller, with todays examples used on the A400M and AN-70.
why would we choose to have all the blades hanging outside the duct for what is basically a turboprop wanting to go fast?
Because it's an alternative drive arrangement for advanced blades. It achieves the goal stated in the beginning, just as the propfan does.