In general, no.

In specific, yes:

• Families, Apple accounts for children don’t need a phone number. https://support.apple.com/en-us/108380
• Education - bulk setup is available through ASM https://support.apple.com/guide/apple-school-manager-m/welcome/web
• Business (or organization, charity, NGO, etc…) - bulk setup is available through ABM https://support.apple.com/guide/apple-business-manager/welcome/web

Posting this here in case there's anyone else out there who doesn't use Apple devices, but needs to create an Apple ID and access the Apple app store.

I eventually succeeded in creating an Apple ID via the Create Your Apple ID web interface. (It seems Apple didn't like something about the phone number I was initially using to confirm my account… but not sure what.)

After that, however, I faced a new problem.

I want to use ipatool to extract iOS software package distributions from the Apple app store, but after authenticating, ipatool was giving me errors like the following…

$ ipatool search "keywords on app store"
ERR error="you have not used this Apple ID on the app store before"

It seems Apple really wants to prevent me from accessing the app store until it thinks I have an actual Apple device linked to my account. (Eesh, what control-freakery .)

So then I tried logging in to my new Apple ID on the web, and browsing the web interface for iOS apps on https://apps.apple.com … but this still didn't enable ipatool to work.

However, I eventually discovered a solution.

I visited https://music.apple.com, and used my new Apple ID to sign in, and… then ipatool started working with my Apple ID.

Happy hacking.

You can use the same phone number for two different Apple IDs. If you want anonymity, you'll want to acquire a second phone number.

In the example you provided, since your computer is registered to show your SMS numbers then the computer is one of the "2nd factors" alongside the phone. If you don't want SMS 2FA you'll have to set up a security key.