backing up a stolen phone

"backing up a stolen phone: [...]if my device can be erased remotely it should be able to be backed up remotely."

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Troubleshooting a Stollen Device:

You cannot backup an iPhone remotely. You can export the data, but if not connected to iCloud, then nothing will be syncing.

Lock with Find My:

A. Erase this: Erase a device in Find My on iPhone - Apple Support. You'll likely never get it back. So, I'd say erase it.

B. Secure your Info:

If concerned for device access, then (A)verify your devices, and (B)modify your credentials. Open a new eMail address and use that for your Apple ID.

1. Verify your Devices:

Verify that all devices are logged in to your account, by using this link: Check your Apple ID Device List to See where you're Signed in - Apple Support

then...

2. Modify your Credentials:

Having been stollen, someone lily has your credentials. So, by all means, modifying them.

• Modify: your login credentials (Using Both a New eMail and a New Password for each and all sites)
• Associate: a different method of payment to your account
• Enable: Two-Factor Authentication for Apple ID and for all other accounts that have such an applicable option

C. Report Items to Apple:

So, report phone call's and messages info to Apple and modify. Use my User: Using the Photos App to Report Scams - User Tip

Hi MeriouslyMan,

Thank you for participating in the Apple Support Communities. We understand your iPhone was stolen and you'd like to backup your data. You would have needed to create a backup prior to having your iPhone stolen. This article explains how if needed in the future: How to back up your iPhone, iPad, and iPod touch.

Also, this article has some steps that may help with locating your iPhone: Find your lost iPhone or iPad with Find My.

If you'd like to leave Apple feedback about this, the best way to make your voice heard is by using this link: Product Feedback - Apple.

Take care.