No, that is the other end of the spectrum like Monty Pyton and other such nonsense that is over there on your isle. You guys don't have anything in the middle, its one extreme or the other. Both of which are too much strangeness for most of us Americans, not yanks thank you very much, to apeal to.
We certainly do have something in the middle. It's simply too specialised & doesn't export well. I don't expect you to understand or enjoy our jokes any more than I understand most of yours. The late Bob Hope never made me laugh once although he was born in England & was obviously a very clever & talented comedian. His was what I would call typical American humour. He employed a lot of British gag writers over the years including the late Bob Monkhouse - a very talented comedian in his own right. He said that he had to completely change his method of writing for US audiences so they could understand the humour. Some of the more recent American comedians have a definite British slant to their humour which is where the subtlety comes in.
The term Yank might not be accurate in all cases but it's an affectionate term for all Americans since they served here in WWII.* It's not intended to be offensive any more than the term Limey or Tommy for a Brit. The sooner people understand that the better we will understand each other.

*PS. There was even a popular song entitled "Over There" used as a march by US forces during WWI. It was composed by an American, George M Cohan, who was awarded the Congressional Medal of Honor for boosting wartime morale. The chorus "The Yanks are Coming" was used as a title for a book & a film.
Over There
Johnnie, get your gun,
Get your gun, get your gun,
Take it on the run,
On the run, on the run.
Hear them calling, you and me,
Every son of liberty.
Hurry right away,
No delay, no delay,
Make your daddy glad
To have had such a lad.
Tell your sweetheart not pine,
To be proud her boy's in line.
(chorus)
Johnnie, get your gun,
Get your gun, get your gun,
Johnnie show the Hun
Who's a son of a gun.
Hoist the flag and let her fly,
Yankee Doodle do or die.
Pack your little kit,
Show your grit, do your bit.
Yankee Doodle fill the ranks,
From the towns and the tanks.
Make your mother proud of you,
And the old Red, White and Blue.
(chorus - twice)
CHORUS
Over there, over there,
Send the word, send the word over there--
That the Yanks are coming,
The Yanks are coming,
The drums rum-tumming
Ev'rywhere.
So prepare, say a pray'r,
Send the word, send the word to beware.
We'll be over, we're coming over,
And we won't come back till it's over
Over there.