Why can't I change the Apple ID on my iPhone?

There's various ways to interpret what you are asking.

Read this document to learn how to Sign out of your account on your iPhone --> Sign out of iCloud on your iPhone, iPad, iPod touch, Apple TV, or Mac - Apple Support

If an app or feature on your device is not working or is restricted, it may have been disabled using Screen Time, or by an IT administrator if you are using a device owned by an employer or educational institution. See how to use Screen Time on an iPhone, iPad, or iPod touch by clicking here --> Use Screen Time on your iPhone, iPad, or iPod touch - Apple Support

Do you mean use your phone to change your Apple ID email address? Here's how you change the email address you use for your Apple ID:

1. Go to https://appleid.apple.com and sign in.

2. In the Sign-In and Security section, choose Apple ID.

3. Enter the email address that you want to use as your Apple ID.

4. Choose Change Apple ID.

5. If you changed your Apple ID to a third-party email address, check your email for a verification code, then enter the code. Learn what to do if you didn't get the email. --> If you didn't receive your verification or reset email - Apple Support

6. If you use services like iCloud or Messages to share with friends and colleagues, sign in to those services with your updated Apple ID. --> What to do after you change your Apple ID or password - Apple Support

For more details, read the document: "Change your Apple ID" --> Change your Apple ID - Apple Support