Searching Contacts by phone number doesn't search "phone" field

When looking up a contact on my iPhone with iOS version 16.7.10, I can enter the last four digits of a phone number in the Search box, and any contact with a phone number containing that sequence of digits will be listed, if the matching phone number is labeled mobile, home, work, main, home fax, work fax, school, or pager. I can also search for a contact by entering the last four digits of a phone number that has a custom label, such as "Customer Service" or "Billing Center" or "after hours".

However, contacts with a matching phone number that is labeled "phone" won't appear in the search list. Why is that? Is there a way to make them show up?

[Re-Titled by Moderator]