It also becomes Apple's problem if a person loses control of an account. Then Apple has a scammer or hacker operating on your account coming from their system. Kind of like you having a spare room in your house and then finding somebody was operating a drug ring out of it. Also people tend to immediately blame Apple if something goes wrong with their account. In the end Apple has to clean up the mess. Account security is just part of 21st century technology. The additional verification is because email accounts alone are not sufficiently secure. People forget their sign in information, or use a password such as "Liberty" or "Freedom" which any halfway competent hacker can find out in a few minutes. Hence the two-factor element with a verification code.
Read the article: Get a verification code and sign in with two-factor authentication - Apple Support
If you're having problems keeping track of accounts in your family there's multiple ways to get a code, and also designate others as sources for a code. Being offered to just use a telephone number is just an alternative. What you are seeing is discussed in this Apple article: Get a verification code and sign in with two-factor authentication - Apple Support
With two-factor authentication you may need to verify your identity using a trusted device generating a verification code when trying to conduct certain activities. 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. Enter the telephone number as requested by the hint.
The article also describes other ways to verify with a trusted device or an Account Recovery Contact. Tap “forgot” to see some of these.
If you had set up an Account Recovery Contact ( Set up an account recovery contact - Apple Support ) you can also get a code that way.
In a situation where a non-functioning device with cellular service was the only trusted number, transfer the cellular service to another device so you can receive a verification code on the other device instead.
If you can’t sign in, get access a trusted device, reset your password, or receive verification codes, you can request account recovery to regain access to your account. This article explains how to recover your Apple ID after a waiting period - How to use account recovery when you can’t reset your Apple Account password - Apple Support One tip to using account recovery it to look for options in small blue letters beneath the normal log-in items if you cannot complete the requested information. The post by shoeluvr13 at this link provides additional detail about the account recovery process: Activation Lockout Issues - Apple Community
You should consider making sure you have multiple trusted devices and telephone numbers (ask a friend or a relative).
You may also wish to read the articles 'Two-factor authentication for Apple ID' ( Two-factor authentication for Apple Account - Apple Support ) and 'Get a verification code and sign in with two-factor authentication' ( Get a verification code and sign in with two-factor authentication - Apple Support ). Various sections contain information that is useful in understanding about the trusted devices (an iPhone, iPad, or Mac that Apple knows is yours) system, and how to get a verification code on a trusted device or at a telephone number.
