Why didn't Harry Potter use the Disillusionment Charm?

Question

In Harry Potter and the Deathly Hallows, Hermione suggests that her and Harry use the Disillusionment charm on themselves when they go to visit Godric's Hollow. In my opinion, I think this would've been a better idea than using the invisibility cloak as it was stated that as they grew older that they had trouble fitting themselves underneath it.

Why didn't Harry take up Hermione's offer of using the Disillusionment charm rather than using the invisibility cloak all of the time, and why was it that the invisibility cloak was so valued when the Disillusionment charm existed?

Answer 1

The cloak is better for moving around in the open.

The Disillusionment Charm works by mimicking the appearance of background objects and patterns:

Harry looked down at his body, or rather, what had been his body, for it didn’t look anything like his any more. It was not invisible; it had simply taken on the exact colour and texture of the kitchen unit behind him. He seemed to have become a human chameleon.

— Order of the Phoenix, chapter 3

By its nature, this method is most effective when the Disillusioned person stays very close to the background and remains still, so that there are no telltale shadows and no parallax effects due to a changing angle of observation, and so that imperfections in the mimicry are not made more apparent by movement. Harry's cloak does not have this restriction; it renders the wearers completely transparent. As long as wind and aerodynamics (Order of the Phoenix, chapter 3) — and the number of people to conceal — are non-issues, the cloak is the better choice.

Although a relative novice such as Goyle can cast a Disillusionment Charm that will work under ideal conditions (Deathly Hallows, chapter 31), only experts have demonstrated the skill to make them effective under more varied conditions.¹

Hermione used Disillusionment (as well as several other charms) to conceal the renegades' camp (Deathly Hallows, chapter 15), but this was out of desperation rather than confidence in the charm's suitability for that situation.

In the book, Harry and Hermione used Polyjuice Potion to appear as Muggles (Deathly Hallows, chapter 16) even while hidden under the cloak. Although Disillusionment underneath the cloak would have made their invisibility coverage slightly more reliable around the ankles, Polyjuice increased their options for staying safe by giving them an entirely different way of blending in. Since the Disillusionment Charm can be slow to remove (Order of the Phoenix, chapter 4) — slower than removing the cloak, at least — it could have hurt their chances of a quick getaway.²

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¹ Moody, Order of the Phoenix, chapter 3; Dumbledore, in the room of the Mirror of Erised, cited by Harry in Deathly Hallows, chapter 22; Voldemort, Deathly Hallows, chapter 24.

² It can be done quickly, such as when Moody and the others arrived at the Dursleys' house (Deathly Hallows, chapter 4), but a lot of expert attention and planning had gone into every detail of that mission.

Answer 2

TL;DR

Lack of creation knowledge, inferiority over the Cloak and habit

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I think that there are three main reasons that made Harry use the Cloak of Invisibility all the time.

1. Harry might not know how to perform a Disillusionment Charm.

To my knowledge, we don't see Harry casting it in the entire series. If he had to have Hermione along with him all the time to cast it, this would create a serious drawback in possible combat situations. Of course, Harry and Hermione were together in the entirety of Book 7 but asking her all the time to perform it on him or them, while he didn't know/want to know how to cast it, would be, at best, childish.

2. The Cloak of Invisibility might be superior over the DC, in combat.

Remember we are in the middle of the Second Wizarding War. Harry didn't just wanted to be invisible to eavesdrop or make fun of someone. He wanted to be unnoticed and probably unharmed by the Death Eaters and other threats. The Cloak, being one of the Deathly Hallows, is "dipped" in magic that makes summoning impossible to uncover those hiding underneath it.

Harry seized Ron’s wrist as he raised his wand. There were too many of them to Stun, even attempting it would give away their position. One of the Death Eaters waved his wand and the scream stopped, still echoing around the distant mountains.

‘Accio Cloak!’ roared one of the Death Eaters.

Harry seized its folds, but it made no attempt to escape, the Summoning Charm had not worked on it.

_{Harry Potter and the Deathly Hallows}

What we should take into account, is that the Cloak cannot be penetrated by charms and jinxes that point to the cloth itself, not the wizard underneath it. An Avada Kedavra would instantly kill Harry, but it would leave the Cloak intact. The Cloak cannot be ripped apart, burnt, summoned or destroyed, thus giving an obvious advantage over the Disillusionment Charm, which would just render the outer "surface" of someone invisible.

3. Harry might just wanted to use it out of habit.

Although he would know that DC would be quicker and without the overhead of a cloth on top of him, Harry was used to use it for seven years and seemed to him more natural to run around under the Cloak than suddenly becoming "vulnerable", with just an intangible charm separating him from revelation.

Now, taking all these points into account, I think that the most likely candidates are 1 and 3. Although 2 is the most rational of the three, Harry didn't know until the very end that his own Cloak was one of the Deathly Hallows. He might have witnessed its effects over the years but I think that his final choice was a mix of stubbornness to learn an alternative way to be invisible and total habit.