Should Usyk fight Itauma?

The short answer is no.

Most of us knew, going into the White vs Itauma fight, that the result was a forgone conclusion. The only question was, when?

You could say White, at 37, was a shot fighter, and that could very well be the case. White, to his credit, has fought a resume of tough opposition and done well, has nothing to be embarrassed about, and had a career that 99% of the pros wish they had. He should enjoy retirement.

THE HARD PUNCHERS

Here's what's frightening about Ituama's punching power though.
There are, generally speaking, three types of "power punchers".
First, there are the guys that wear you down to the point that the final 'coup de maitre' is more a stoppage of attrition. 
Then there's the one punch guys that can take you out with one clean shot. But, those guy typically have to have full commitment into the punch, and full commitment to the punch tends to be accompanied by defensive openings which can be countered.
Itauma is one of the very rare guys that don't have to fully commit to a punch, and thereby not be open for a counter, in order to hurt you.
The only other fighter that comes to mind in recent years was a young Gennady Golovkin.

ITAUMA NOT READY FOR USYK?

When people say that Itauma isn't ready for Usyk, I'd say Usyk isn't ready for Itauma. 
Let's talk about experience. Itauma had a fairly limited amateur career while Usyk was an Olympic gold medalist. Usyk has also fought the top guys in the heavyweight division, and beat them twice, while Itauma's best win was against an aging Dillian White. 
Normally things would heavily favor Usyk but when a fighter has the type of power that Itauma has, it tends to negate much of that experience. 
So how do you beat guys like Itauma and Golovkin? 
Two ways, either a) you either let them get old, as in the case of the latter, or b) you fight the fight of your life (think Leonard vs Hearns).

NOT GETTING HURT DOESN'T GUARANTEE WINNING

At 38, will Usyk have the endurance, no matter how good his conditioning training regimen is, to wear down a 20 year old? Highly unlikely.
So without conditioning it's going to be a game of make him miss make him pay (but not making him miss gets you out of there), can Usyk do that for 12 rounds? 
Possibly.
But even if he is able to, that doesn't mean he wins the fight. Who was pressing the action, who was running, who landed more etc comes into play and not getting hit isn't guaranteed to result in a win.

Basically there are too many scenarios for Itauma to win and too few for Usyk to win.

SO WHO SHOULD USYK FIGHT NEXT?

First of all, retirement is not a bad option. You're 38 years old, you've beaten the best in the division, you're undefeated, and an argument can be made that you're the best heavyweight ever. (not claiming he is but you could make a legitimate argument).
If you still have the burning desire to fight a big fight, fight Joseph Parker.
Parker is a big tough heavyweight with a glowing resume and a sizeable following. It'll be a big fight but I don't know that Parker is any better than Joshua or Fury, possibly not quite as good, so it's a winnable fight against someone not as dangerous as Itauma.

And then retire.

If you cannot help yourself and have to fight Itauma, fight him in his very next fight. Any more fight experience this kid gets increases his proficiency while age decreases yours.