When leaving Privet Drive, why did there need to be seven Potters instead of using the Invisibility Cloak or Disillusionment Charms?

In Harry Potter and the Deathly Hallows, a bunch of the Order of the Phoenix members show up to escort Harry to the Burrow. The rationale behind this was that they couldn't use the Floo Network, they couldn't Apparate, they couldn't use a Portkey, and Harry still had the Trace on him. Thus, they were all going to fly away, and have six decoys plus the real Harry Potter.

What I don't get is this: Why didn't Harry just put on his Invisibility Cloak and walk out of range of the charm, and then Apparate away? He's largely undetectable under the cloak, and as long as he were to get out of range of the Floo/Apparition restrictions, he could've met up with a couple of Disillusioned or invisible Order members and been on his merry way. Why didn't he?

Answer

Deathly Hallows indicates that the Seven Potters wasn't the first plan to escort Harry away from No. 4 Privet Drive.

[...]Hagrid said, “All righ’, Harry? Ready fer the off?”

“Definitely,” said Harry, beaming around at them all. “But I wasn’t expecting this many of you!”

“Change of plan,” growled Mad-Eye [...]

Deathly Hallows - page 45 - US Hardcover

The Seven Potters was Dumbledore's plan. He told Snape the true date that Harry would be moved from Privet Drive, so that Snape could pass the information along to Voldemort. The goal was to keep Snape's cover intact, Harry safe, and Hogwarts out of the control of the Death Eaters (the Carrows), and Dumbledore condoned this. He instructed Snape to Confund Mundungus Fletcher and feed the idea of the Seven Potter to Dung, and to plant the idea of Dung suggesting the Seven Potters plan to the Order of the Phoenix.

“You will have to give Voldemort the correct date of Harry’s departure from his aunt and uncle’s,” said Dumbledore. “Not to do so will raise suspicion, when Voldemort believes you so well informed. However, you must plant the idea of decoys; that, I think, ought to ensure Harry’s safety. Try Confunding Mundungus Fletcher. And Severus, if you are forced to take part in the chase, be sure to act your part convincingly. . . . I am counting upon you to remain in Lord Voldemort’s good books as long as possible, or Hogwarts will be left to the mercy of the Carrows. . . .”

Now Snape was head to head with Mundungus in an unfamiliar tavern, Mundungus’s face looking curiously blank, Snape frowning in concentration.

“You will suggest to the Order of the Phoenix,” Snape murmured, “that they use decoys. Polyjuice Potion. Identical Potters. It is the only thing that might work. You will forget that I have suggested this. You will present it as your own idea. You understand?”

“I understand,” murmured Mundungus, his eyes unfocused. . . .

Deathly Hallows - page 688 - US Hardcover

Edited to Add: Harry was sixteen on the day the Order moved him to the Burrow. Apparition requires a wand. If Harry had Apparated without a license, using his wand, he would have tripped the Trace because he was under the age of seventeen. Remember, Harry turns seventeen while at the Burrow. The decision to take Harry from Privet Drive before he was seventeen was a risk, because the moment Harry left the Dursleys' home without the intention of ever returning or considering it home, Lily's protective enchantments broke.

The Homenum Revelio spell could have revealed Harry's presence to the Death Eaters, if they had formed a perimeter around Privet Drive to monitor Harry's movements, even if he were under an Invisibility Cloak and that would have left Harry quite vulnerable.

Invisibility Cloaks are not, generally, infallible. They may rip or grow opaque with age, or the charms placed upon them may wear off, or be countered by charms of revealment. This is why witches and wizards usually turn, in the first instance, the Disillusionment Charms for self-camouflage or concealment.

Tales of Beedle the Bard - page 163 - US Collector's Edition

Why didn't the Order use Disillusionment Charms to get Harry out of Privet Drive and to the Burrow? I don't recall any instance in canon (and correct me if I'm wrong!) where Harry casts a Disillusionment Charm on himself. However, in Order of the Phoenix, Moody places a Disillusionment Charm on Harry in the chapter The Advance Guard, so it's unclear why they could not have employed this on top of or in lieu of the Seven Potters. According to Moody, Harry's Invisibility Cloak would have come off during the flight if he rode a broom while wearing the cloak.

‘Disillusionment Charm,’ said Moody, raising his wand. ‘Lupin says you’ve got an Invisibility Cloak, but it won’t stay on while we’re flying; this’ll disguise you better. Here you go –’

Order of the Phoenix - page 53 - British Hardcover

The Disillusionment Charm does not create invisibility (except for Dumbledore; see Tales of Beedle the Bard, page 163) but rather allows a witch or wizard to blend in with his/her surroundings, like a chameleon:

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 - page 54 - British Hardcover

I suppose I would ask Why not a Disillusionment Charm, rather than the Invisibility Cloak? Further, we don't know exactly when the Taboo was placed on Voldemort's name. Harry, not afraid to say 'Voldemort,' might have uttered the word at the wrong place and time, which would have led the Death Eaters right to him, cloak or no cloak. The breaking of Lily's enchantment was a big vulnerability for Harry.