Forgot Apple ID Password. Account Recovery Annoying.

It's an unfortunate situation, but the account recovery process is industry standard for two factor authentication security. Account recovery is automated and can be just a couple days to several weeks depending on many factors for each situation. Even Google, banks, Yahoo, Samsung, etc. now encourage and use this process because scammers are getting smarter and smarter. Two-factor authentication for Apple ID - Apple Support

Your other options are:

1. Set up a recovery key for your Apple ID - Apple Support A recovery key is an randomly generated 28-character code that helps improve the security of your Apple ID account by giving you more control over resetting your password to regain access to your account. However, if you lose your recovery key and can’t access one of your trusted devices, you'll be locked out of your account permanently.
2. About Security Keys for Apple ID - Apple Support A security key is a small external device that looks like a thumb drive or tag, which can be used for verification when signing in with your Apple ID using two-factor authentication. You're responsible for maintaining access to your security keys. If you lose all of your trusted devices and security keys, you could be locked out of your account permanently.

KatS182 wrote:

I just recently purchased the iPhone 14 Max and traded in my old iPhone. My password was of course located in the old iPhone which the store had to reset. I tried resetting my password during the setting up phase of the new iPhone thinking it would be simple with a few verification procedures. This thing took me to account recovery which told me I had to wait 24 hours to receive a time frame of when I'd be able to reset MY password. After waiting 24 hours I am told I have to wait an additional 3 days to reset the password. Why is this process so frustrating. It's irritating enough that I'm unable to get into my account and access any of my old information. On top of that, I now have to wait several days??? This policy is ridiculous. Apple needs to find new ways to help the community with their account recovery. Ask me anything about my account so that I may access my information. It shouldn't take 72 hours.

Is it Apple's fault that you can't remember your own Apple id password.

Quick to lay blame on others but not yourself.

It is their policy whether you like it or not.