We all know Jon introduced this song as being about the Soul Kitchen, but I've really failed to find a connection to it that way. Come On Up To Our House seems much more fitting to that topic for me.
Now as we know from the past - Jon has changed the themes of some songs just as it fitted the occasion. I vaguely remember him talking about These Days (the song) in one interview about him making fun of one of their record managers (with reference to the 2nd verse):
"...At one moment I sing 'Jimmy Shoes busted both his legs'. Jimmy Shoes is the nick-name of Jimmy Iovine, the big-boss of Interscope Records, but in my song he's just a little boy. A little boy that breaks both of his little legs. Ha ha!"
Later on during concerts he gave speeches about it referring to "Generation X" and trying to make ends meet and so on.
Or more recently: Superman Tonight. When TC was released it was "the only boy-girl song on the album". Later on it had an "immense social aspect and conscious undertone", so that they could promote the video of it that way.

Getting back to All Hail The King. I actually think it's about Richie and deals with his departure in quite a harsh way, which at the same time makes it seem reasonable that Jon has brought up a different background story for the song.

Let's dig into the lyrics:
Heavy is the head that wears the crown
--> a "heavy head" is (at least in the German language) a reference to having a hangover

All the people came to hear him
Speak from miles around
They hug on every word
A song in every sound
Heavy is the head that wears the crown
He touched the sky to light up
All the stars
He could snap his fingers
And catch lightning in a jar
--> this refers to Richie's prime era where he could do magic with his guitar playing and stun everybody - let's say it's the mid-90's

I am you and you are me
--> still the band's prime and the time where they really were at their peak as colloborators

And we are who we are
--> "who we are" might lead to the Jersey-underdog attitude "us against the world"
Touch the sky and light up all the stars

CHORUS
All hail the king whose castle’s falling down
--> Richie's descent as a guitar player and maybe as a friend and human being. The King might be a reference to the old nickname (King of Swing)

The paper prince who wears a cardboard crown
Poor man has his money
Rich man has his gold
All hail the king whose fortune
Is his soul
--> I think that these three lines are just a comparison. What's money for the poor man is the gold for the rich and was the soul to Richie's guitar playing

He climbed the clouds
To heaven’s highest hill
--> the band's rise to fame and stardom

When you get that high
The earth below looks just like a blue pill
--> Richie lost some of his down-to-earthness as the band continued to be successful

Gave wind to all his horses
And to all his men good will
When he climbed down from heaven’s
Highest hill
--> he abandoned the band and I guess this passage refers to his decline with his constant boozing issues during the last 2 tours he was on board with the band

All hail the king whose castle’s falling down
The paper prince who wears a cardboard crown
Poor man has his money
Rich man has his gold
All hail the king whose fortune is his soul
He breathed his last

They laid him in the ground
False prophets spoke of riches
And said all hail to us now
--> the harshest part of the song and it may hint to Richie's circle of friends (Nikki Lund etc.) leading him onto the wrong path

The faithful wouldn’t listen
And they never would bow down
He breathed his last
They laid him in the ground
--> "the faithful" are the band who didn't stop touring because of him and have moved on since. Especially since it seems that Jon really doesn't see a future for Richie with BJ anymore.

All hail the king whose castle’s falling down
The paper prince who wears a cardboard crown
Poor man has his money
Rich man has his gold
All hail the king whose fortune is his soul


Of course that's nothing but my personal interpretation and pure speculation. But I see the song in a whole different light since then and it became much meaningful to me.