Values instead of designators on assembly drawing
You are missing several somethings:


Values are generally longer than the designator (R1 as opposed to 100K, or U1 as opposed to dsPIC30F3013) so the designators take up less space.
Values may change though the part designator is the same.  Say you discover that R1 needs to be 90K instead of 100K.  If you have values on the board, you now get to scrap all your boards and have new ones made with the correct value.
As Brian Drummond mentioned in a comment, you may have 30 parts with the same value.  How do you locate the correct one when comparing the board with the schematic?  How do you tell a technician to replace a particular resistor with a different value?  Saying "replace R17 with a 15k" is much easier than saying "that 10K resistor over there, beside the 5 capacitors and lower down than the inductor needs to be replaced with a 15K."
As Asmyldof mentions in comment:  The value itself often isn't worth much.  The designator refers you to the parts list where you see that C1 isn't just a 1nF capacitor as you could see from the value.  It is also (and much more importantly) an X1 rated capacitor safe for use in power lines.  Which value would you print on the board?  The capacitive value, or the voltage it is rated to safely handle?
A final thing that probably doesn't weigh as much as it used to is manually inserted parts.  You are asking a bit much of an uneducated factory worker for them to understand the values.  They used to have manual insertion stations where there was a tray of parts marked by the designator.  The workers looked at the board and saw, say, R5 and pulled a part out of the R5 hole in the tray and put it in the board - and never knew the difference between a resistor and a capacitor and didn't care.  Tab A in Slot A and on to the next part.


Number 4 is one I hadn't really thought of until Asmyldof mentioned it, but consider a capacitive drop power supply with a 33nF capacitor providing the drop, and another 33nF capacitor used in the low voltage section.  How do you represent that in your assembly drawing when you use just the value?  That 33nF in the dropper had better be safety rated, and you'd better not mix it up with that other 33nF that isn't safety rated.  The designator saves your bacon again by referring you to the BOM where you see that C1 is 33nF X1 and C10 is 33nF and rated for 25V.