Is there any way to have an email sent for verification instead of a text?

What if I can't access a trusted device or didn't receive a verification code?

If you're signing in and don’t have a trusted device handy that can display verification codes, you can have a code sent to your trusted phone number via text message or an automated phone call instead. Click Didn't Get a Code on the sign in screen and choose to send a code to your trusted phone number. You can also get a code directly from Settings on a trusted device. Learn how to get a verification code.

If you use iOS 11.3 or later on your iPhone, you might not need to enter a verification code. In some cases, your trusted phone number can be automatically verified in the background on your iPhone. It’s one less thing to do, and your account is still protected with two-factor authentication.

If you lost / can't reach the trusted device or phone number associated with your Apple ID

As long as you still have your Recovery Key and remember your Apple ID password, you can sign in and add a new trusted device or phone number to your account. You can also remove any devices you may have lost, sold, or given away.

1. Go to your Apple ID account page and enter your Apple ID and password.
2. On the Verify Your Identity screen, select "Can’t access your trusted devices?"
3. In the pop-up window, enter your Recovery Key.
4. Go to the Security section and click Edit.

Remove the device you no longer wish to use to verify your identity. If you have additional devices with Find My iPhone enabled, you can verify them as trusted devices. You can also add additional trusted phone numbers.

If you lost your Recovery Key

As long as you remember your Apple ID password and still have access to one of your trusted devices, you can sign in and create a new Recovery Key.

1. Go to your Apple ID account page.
2. Sign in with your password and trusted device.
3. In the Security section, click Edit > Replace Lost Key.

Keep your new Recovery Key in a safe place. Your old Recovery Key won't work anymore and you can't use it to reset your password or access your account.

If you can't sign in with two-step verification using your Apple ID ...

Skip Edwards wrote:

If anyone breaks into the phone with the password and changes the password for Apple ID, having a text sent to that phone makes it easy for that person to continue. If the verification code is sent to an email that the person cannot access, it seems it would be more secure.

Even if someone did get into your phone using your device password, they would still need your Apple ID password in order to change the Apple ID password. This seems like a very unlikely chain of events.

Use a complex passcode on your phone if this is of concern to you.

That WSJ article is making the rounds including Apple News. It said:

"With knowledge of the iPhone's passcode, a thief can easily reset the victim's Apple ID password in the Settings app, even if Face ID or Touch ID is enabled. Subsequently, the thief can turn off Find My iPhone on the device, preventing the owner of the device from tracking its location or remotely erasing the device via iCloud. The thief can also remove other trusted Apple devices from the account to further lock out the victim."

If your iPhone is a Trusted Device (as it likely is) then that seems plausible. I have not tried this but per Apple:

Reset your Apple ID password on your iPhone or other trusted Apple device:

Go to Settings. Tap your name > Password & Security > Change Password.

Follow the onscreen instructions to reset your password.

Apple's response to the WSJ article:

"We sympathize with users who have had this experience and we take all attacks on our users very seriously, no matter how rare," the spokesperson added. "We will continue to advance the protections to help keep user accounts secure."

In a tweet, the WSJ recommended that Apple add extra protections to iOS and introduce additional Apple ID account recovery options.