The standard answer is Brevity. That is, it cuts down on the amount of radio time used. In the case of my department, until the MCT's came online, you would have a difficult time getting on the air with so many deputy's and so much radio chatter during peak times. The 10 signals and coding of calls to dispatch really help.
When we clear a call, we code the dispisition. Example, an alarm at a residence is a 2-0, if it is false E, backup used 3, and officer assaulted code a 0. So you would call in 10-98 copy code. Dispatch would acknowledge 10-98 go ahead with code. You would reply 2-0-E Edward-3-0.
I can then go back into the MCT call history and see how you have cleared each call.
It seems kinda cumbersom, but it really makes a difference if your radio is at about max as ours is.  

Tradition is a large part of it. It is like the story of the Royal Army going over their crew drills in the 1920s. They had to call in some really old decrepit veterans to tell them what some parts of the drill meant. In one rather telling case, during an artillery drill, two soldiers were posted on either side of the field piece during the drill, and just stood there the whole time, doing nothing. When one of the old vets was queried, he told the assembled staff officers that the two soldiers were there to "hold the horses." Large organizations often have wierd rituals that no-one can effectively trace or explain. Anthropologists could have a lot of fun in a medium to large-sized police agency, figuring some things out. The halmark of a good organization is the ability to analyze this kind of stuff and easily discard it.

Our agency, at least, has gotten rid of many 10-codes and uses more and more plain text. Some codes are still used, however, for brevity and clarity, and we also have several non-standard codes, which change periodically, for sensitive information and officer safety issues. Bad guys know the "standard" 10-codes, too, and I have seen a few situations go south when the radio suddenly blares "your subject is 10-99 (wanted)," and the bad guy knows exactly what that means.

10 codes as well as Signal codes are "supposed" to make radio traffic shorter, eliminate any gray areas in language, and also to keep any suspects near your radio to know what you or dispatch is saying.

Us city guys use only 10 codes but our county guys use both 10 codes as well as Signals.  I personally don't see the point in the redundancy.

We have 100 10-codes ranging from 10-0 to 10-99.  There's only a handful, maybe 10 at the most that we use on a normal basis.

Man...nobody I know of has used 10 codes for years.  

I really do not know, someone in authority had too much time on there hands and it became standard, I cannot say it was for brevity as here is an example- sixty three (vs) traffic stop, they are both the same in Ohio, and both mean the same thing.  And sometimes it is even longer as proper radio terminology is signal-63 five syllables vs the three for traffic stop. Then there are the codes i.e., code 10 (means send back up) when you could just say send back up . I think as someone has made a point, some places are getting away from the numerical codes and going with plain english, it helps on cross radio traffic as a 31-A for Ohio Sheriffs means disabled motor vehicle, but for the Ohio State Patrol it means accident with injuries. Say "what you mean" does have its valid points. Secret transmissions, not a good point as any bad guy knows when your having problems and you use the radio, that your calling for the calvary. There is a code that meant , don't let the person your with hear the following from dispatch, this was the only code I felt that had any real use.

We still use our ten codes.   We shorten most of them.  as in;  279 PD, 98   or  279 to 280; give me a 21.  or, let's 49 at shipley's.  the radio opperators still use the tens.  Some times, it's needed.  I'd rather have a BG hear  "are you 10-12?"  than "do you have a secure radio?"
all of our "sensitive" traffic is scrambled.  anything that is not a commonly used code is plain english.  we use maybe about 30 of the hundred.
some of the calls that require a little professional descreetness get the codes too.
What sounds better on the radio 10-69 or dead person?  10-60 or mental subject?
I think we still need the codes we use, but the rest stick around for tradition's sake.  Hope this helps....

Combining plain english and radio codes is a problem for every agency.

If you need a 960 dont say "I'll take a 960" just say "960". Only when radio codes are improperly combined with plain english, do they become more wordy than plain english.


There is the secretive factor too. When I'm standing next to a 3-striker I would rather have dispatch say "10-32F" than "Hey barney, that guy you got there is a 3 time loser with a felony arrest warrant, maybe you should hook him".

"120- Signal 6"
"130-120, go to Common Channel"
"Hey Vern, where you going for dinner"
"I dunno, wanna join me?
"Sure, I just need to pick up my dry cleaning"
"No problem.  Where you wanna go?"
"I don't care.  Grandy's gives discounts..."
"Sounds good.  I'll stop by the house.  I think my wife has some coupons in the coupon book my kid sells at school"

And so on and so on.  This is why I hate 10 codes, signal whatevers, and code whatchacalls.  We think it's important to keep "brevity" and professional on dispatch, field operations, etc.  But when you switch to a common (ie. bullshit) channel no one cares.  These can be just as easily monitored by dispatch, supervisors, and the public.  I hate 10 codes.  I wish they would just go to 10-code heaven.

Well, I would rather get this while standing in front of the violator while he can hear it as well as I can:

1C**, copy 10-38F 10-51, 10-27 Sam, the vehicle is 10-40, advise when 10-15.

Than this:

Officer *********, copy a felony warrant on your subject, he is dangerous, use caution, also, he has a suspended license.  The vehicle is stolen, advise when your subject has been placed into custody.

That guy would be running halfway through the radio transmission, with me in a foot pursuit.  If I can get any edge on his before he bolts, it is going to be in my favor.  Enough police departments use different radio codes.  That way no career turd is going to be able to memorize all the codes for every department.  

Get the point?