Empty "[Gmail]" Folder in Apple Mail App: I figured out the solution. You have to add an IMAP Path Prefix.

To get rid of this hugely annoying greyed-out [Gmail] folder in Apple Mail on iPhones or iPads, you have to make changes on both the mobile device and your desktop app, as follows...

On your iPhone or iPad:

Go to Accounts > (select the offending Gmail account) > Account Settings > Advanced.

Where it says IMAP Path Prefix, type in: [Gmail].

Then you back one screen (Account Settings) and hit Done to save the change. Back out of the settings screens and close the mail app.

On your Mac:

Next, go to your desktop/cloud app and add this same prefix to any Labels (folders) you have created. Make sure to use a forward slash here "[Gmail]/".

NOTE: Sub-labels (subfolders) do not use the [Gmail] prefix. If you have sub-labels, just use plain names.

Back to your iPhone or iPad:

Once that's all set up properly, you can open your mail apps on iPad or iPhone, and you should see your folders displayed correctly without that annoying greyed-out folder.