As ksbes says, invisibility is a great advantage, but there is another one.

It's magic. Or at least it seams to be magic

any sufficiently advanced technology is indistinguishable from magic

In this case, they don't see any shield, but still, something is blocking all projectiles, and when they try to hit them, there seems to be a wall between them and your soldiers.

Yup, definitely magic, we don't stand a chance to beat them.

On top of any additional answers, two more spring to mind:

1. Undercover agents
Agents working undercover within primitive civilisations may want such protection, but still need to fit in with the natives

2. Obfuscation of possible weaknesses
One of the ways an opponent can find a weakness for a defense is to poke it with different things to see how it reacts. If the shield doesn't give off any kind of visible responses to stimuli, it makes this job almost impossible to perform.

Holding a shield is like an invitation for others to throw stuff at you.

It's a pretty aggressive move actually. You're saying "I know you're violent and I'm prepared." You're telling them you're at war.

An invisible shield protects just as well as a visible one (better actually, because the attackers don't know where the shield stops and starts and can't target unprotected areas) but without the posturing.

As others have mentioned, visibility is important as well. Your vision of potential danger isn't impaired and you are seen in all your glory. It can also be a power play. "I am here, you can see I'm unarmed, and you can't harm me." For a ruler or a higher social class, this posture is invaluable. It sets you up as superior.

I also support Kepotx's answer: making the shields invisible looks like magic to outsiders. If the attackers have a pre-firearms weapon technology, a shield like this would be impossible to understand. Which only reinforces the social stratification.

police is already widly uses transparent riot shildes. The reason is simple: to see through. Invisibility might be just a side-effect of super-transparent technology

Expend that Ammo.

Nothing like letting your opponent waste a lot of ammo (or just stamina) trying to hit you so they run out sooner. Initial reaction : "fire again, I must have missed". Next reaction : "keep firing, we can break through it". Last reaction : "Oh, oh, out of ammo". :-)

Confuse me.

You fire, they should be a mushy pool on the floor and wall and they're just standing their grinning at you, or, a little worse, beating twelve kinds of heck out of you. It's got to confuse a body. Always an advantage in combat.

Hit me, Baby.

A shield is an offensive weapon and experiencing being repeatedly hit by something invisible isn't just confusing, it, well, hurts. You can't really see it to defend so a skilled attacked can beat the stuffing out of an opponent with their invisible shield. And in case you object to this, keep in mind that relativity says there's no fundamental difference between something hitting the shield and the shield hitting something.

Throwing a shield is kinda silly, but it's an option and in this case your opponent can't see to dodge it and can't see to pick it up.

Showing off to the Natives.

If nothing else it's going to be impressive having an invisible shield and it is going to make them ask a rather important question : has he any other stuff that's invisible, like a bloody huge gun or several mates standing nearby armed to the teeth ? So a lot easier to be diplomatic when people are thinking important things like that.

Due to the energy field technology that makes them, the shields are invisible, nearly impenetrable, and very light.

The invisibility allows the user to see through it, increasing visibility.

Nearly impenetrable is obviously a good thing for a shield.

The low weight allows the user to quickly react in a fight.

Because it is invisible by design. Bullets, for example, are invisible by design and we don't really care to make them visible. There are exceptions of course, like tracing bullets and laser pointer thingies but it has not become a norm.

Sun Tzu wrote in The Art of War:

All warfare is based on deception. Hence, when we are able to attack,
we must seem unable; when using our forces, we must appear inactive;
when we are near, we must make the enemy believe we are far away; when
far away, we must make him believe we are near.

This argues strongly that the best thing is to have weapons and forces at hand that the enemy does not know about. It allows plausible deniability about whether one is prepared for combat or not. It allows for secret and undercover agents. It allows one to quickly transition from peaceful diplomacy to combat as needed.

An example from fiction: In Asimov's Foundation and Empire, the "trader" Lathan Devers is taken prisoner and spends most of the book gathering information from the powerful top general and capital of the galactic empire, because he appears effectively powerless. At the climax this happens (Ch. 9):

Devers snarled and reached slowly for his own gun. The lieutenant of
police smiled more broadly and squeezed the contacts. The blasting
line of force struck Devers' chest in an accurate blaze of destruction
-- that bounced harmlessly off his personal shield in sparkling spicules of light.

Devers shot in turn, and the lieutenant's head fell from off an upper
torso that had disappeared. It was still smiling as it lay in the jag
of sunshine which entered through the new-made hole in the wall.

It was through the back entrance that they left.

As it turns out, the entire plot was made possible because Devers had the confidence from a personal (invisible) shield, which the men of the supposedly much more powerful galactic empire did not think was technically possible.