The premise is that the use of the modern language helps connect a modern-day audience to the work.
Consider the following...
We headed over to Nate's pad.
All he had to eat was some gutt waddin' so we decided to bug out.
Monte was doing his usual lip flappin' and I was only paying attention to the cherry Chevy with some gnarly glasspacks.
Since I didn't have no scratch all I could do was cruise with Monte and the other cool heads.
Right on! This would have made sense to someone in the 1960's, but today it just sounds goofy.
Without the 60's slang the storyline would read...
We dropped by Nate's house but we didn't like what he was having for supper so we decided to leave.
Monte wouldn't stop talking and I paid more attention to a new automobile in front of us.
Since I didn't have any money I just spent the evening riding around with Monte and my friends.
I enjoyed myself.
Admittedly this sample was a bit more fun to read in the 1960's version, but you might need a dictionary of 60's slang to figure it out.
One of the primary reasons using slang is a problem is because it has a very short shelf life.
The second issue with slang usage is that while it may seem appropriate to use the slang today, by the time the story reaches the public there will be new words that have replaced the ones you used for your story which will make your 'new' story sound dated.
Slang is often only used successfully in parodies.
If a writing is design to poke fun at something from the past then the use of slang may add to the sense of comic timing, but for most stories slang is generally a bad idea.
When you use straightforward and understandable language your message comes through clearly and will remain clear for future generations of readers.
Many writers who have written with slang generally find their work on a discount table at a dollar store in a very short period of time.
One more time for those playing along at home...
Don't let me cut out thinkin' you got cooties, man.
Make sure your words are outta sight -lay it on me.
Don't let your readers put your work aside thinking your work is ridiculous.
Make sure your words make sense and let that be what impresses your reader.