Merge Apple IDs, as in close one and transfer to the other.

You can't merge Apple IDs. You can try setting up Family Sharing between the IDs if you want to be able to share purchases made with the IDs.

Family Sharing.   *

https://www.youtube.com/watch?v=I6vZd14FsJ4

Family Sharing - Set up.  *

Apple doesn’t routinely monitor the discussions. These are mostly user to user discussions.

If you want to, you can send Apple feedback. They won't answer, but at least will know there is a problem or a suggestion for change. If enough people send feedback, it may get the problem/suggested change solved sooner. Pick the closest topic you can find.

Click here to send Feedback   -

If you forgot the Apple ID (iCloud) password, enter the Apple (iCloud) ID, and click Forgot Password. See if you can get a Rescue or Notification email option. Link to contact Apple Support at the end of the 2nd article.

Apple ID - Manage  -     

Apple ID – Forgot Password  *      

If you want to cancel your Apple ID account, you can deactivate it or delete it.

Apple ID - How to deactivate your Apple ID account.    *

All purchases made using an Apple ID are tied to the ID. Delete the ID and you will need to download them using your new ID. There have been posts by people who have contacted Apple Support and they were told that if you delete an ID associated with an email address, you can never reuse the email address for an Apple ID.  Make sure that you sign out of all your devices to avoid issues with apps that use your Apple ID account or iCloud. After your account is deleted, you can't sign out of iCloud or turn off Find My iPhone Activation Lock on your devices. If you forget to sign out, you might not be able to use your device when your account is deleted.

How to delete your Apple ID account.   *  

Apple ID – How to Delete.  -

Delete Apple ID (new).   -

What to do after you change your Apple ID or password - Apple Support   -

I don't want to use family sharing, I don't have that email any longer so I don't have the password. Apple is so bright why is not able to provide a way for an account to be either merged with another as long as the credentials match or to completely close out the account.

It really isn't that strange. Think of the money apple makes if every legacy mobileme or earlier user (with apple ids that weren't required to be email addresses) throws their hands up in frustration and just purchases all their content again.

There isn't any other reason than that. It's not a security issue, as evidenced by the fact that Apple recommends simply changing the password of you're apple id once someone else has accessed and abused it.

I agree. It really is strange that Apple has not created a fix for this issue that impacts many of us.