Why does my iPhone say the maximum number of free accounts?

To me this looks like an account activation limit, not an account creation limit. It is not the same thing. This is mentioned in the last paragraph of this document: How to create a new Apple ID - Apple Support

"If you created a new Apple ID on the web and see a message that you need to sign in to iTunes, follow the steps below for your device. . . " It then asks you to sign into the account on a device itself. A "Could Not Set Up iCloud" message means you have created Apple Accounts on certain platforms that need to be set up in iCloud too, but you have reached an annual per-device limit for doing this.

See the recommendations in the link under "What you should do" for using a different device to set up iCloud accounts, using an account that is already set up, or by contacting Apple Support:

Click here --> Choose your country or region - Official Apple Support Select your country, then a product. If you don't see one that handles your issue then keep experimenting with selections until you reach one that gets you a chat session or a telephone call and get the representative to redirect you.

or:

Contact Apple for support and service --> "See a list of Apple phone numbers around the world."

Click here --> Contact Apple for support and service - Apple Support

If you need to create another Apple ID, you'll need to do it on a different device.