SEE COMMENTS BELOW:

"I think we have discussed this before"
MANY TIMES, ON MANY POSTS.

"but maybe some clarification is in order"
THIS SEEMS TO BE A CONSTANT SOURCE OF CONFUSION FOR MUSICIANS.

"I don't know how the Major Artists do it but I suspect songs are recorded all the time to see if they want to release the song or songs. If the song is not released for sale no mechanical license would be needed"
MAJOR ARTISTS DON'T GENERALLY PAY THE MECHANICAL RATE. THEY NEGOTIATE WITH THE AUTHOR/PUBLISHER FOR A REDUCED RATE OR FLAT FEE. THE AUTHOR/PUBLISHER IS USUALLY WILLING TO AGREE TO THE REDUCED RATE OR FLAT FEE IN RETURN FOR HAVING THE SONG RELEASED BY A MAJOR ARTIST WHICH AUTOMATICALLY GUARANTEES INCOME. THIS IS ESPECIALLY TRUE IF THE ARTIST IS LIKELY TO GET AIRPLAY BECAUSE THEN THE AUTHOR/PUBLISHER WILL GET PERFORMANCE RIGHTS INCOME ON TOP OF THE LICENSE AS WELL AS THE ADDED BENEFIT OF NUMEROUS OTHER LICENSED RELEASES BY LOWER LEVEL ARTISTS WHICH PROBABLY WOULD NOT OTHERWISE HAVE HAPPENED.

"When songs are pitched to an Artist or Producer and they deem a song or songs to have potential for that Artist they may go into the studio and do a complete master recording of all the songs and then judge all of them to see what will go on an album and what will be passed on"
THEY SHOULD BE DOING THIS WITH THE AUTHOR/PUBLISHERS PERMISSION

"This could be called demo shopping if it is run by a Label head, etc."
I'M NOT SURE WHAT YOU MEAN BY A "LABEL HEAD" SHOPPING A DEMO OR A SONG IS USUALLY DONE BY GOING THROUGH THE A&R DEPARTMENT

"In fact if you pitch songs to an Artist that is shopping a demo to a Label they can do that with the songs that they are considering without any permission from the copyright owner."
NOT LEGALLY, THEY CAN'T, AND I WOULD NOT RECOMMEND RECORDING THE SONG WITHOUT PERMISSION. NOTE THAT PERMISSION IS USUALLY PRETTY EASY TO OBTAIN AND THE RAMIFICATIONS CAN BE SEVERE IF YOU DON'T GET PERMISSION IN ADVANCE. FOR EXAMPLE, WHAT HAPPENS IF YOU SHOP THE DEMO TO A LABEL, AND THEY DECIDE THEY WANT YOU BASED ON THE STRENGTH OF THE MATERIAL. DID YOU DISCLOSE TO THEM THAT YOU DIDN'T HAVE PERMISSION TO USE THE MATERIAL? WERE YOU ACTING UNPROFESSONALLY BY NOT DOING SO? THE RECORDING CONTRACT IS GOING TO REQUIRE YOU TO WARRANT THAT YOU ALREADY HAVE THE RIGHTS TO THE SONGS, AND USUALLY CONTAINS A PROVISION FOR THE LABEL TO PAY LESS THAN THE STANDARD MECHANICAL RATE. NOW YOU HAVE A DILEMMA BECAUSE YOU HAVE A DEAL, AND THEN YOU GO TO THE AUTHOR/PUBLISHER ONLY TO FIND OUT THAT THEY ALREADY MADE AN EXCLUSIVE DEAL WITH SOMEONE ELSE TO BE THE FIRST TO RELEASE THE SONG, OR THEY ACTUALLY SOLD THE SONG (REMEMBER, IF IT'S UNPUBLISHED, YOU CAN'T GET A MECHANICAL LICENSE YET AND THEY MAINTAIN COMPLETE CONTROL OVER THE ORIGINAL WORK OF AUTHORSHIP). OF COURSE, ALL OF THIS COULD HAVE BEEN AVOIDED BY SIMPLY ASKING IN THE FIRST PLACE (AND BETTER THAN THAT, GETTING A WRITTEN AGREEMENT TO USE THE SONG ON A CONTINGENT BASIS).

"It is only when they decide to release the song for sale that they apply for the mechanical license A song is not considered published until it is released for sale."
NOT EXACTLY. SONGS CAN BE PUBLISHED WITHOUT BEING RELEASED FOR SALE IN THE FORM OF A RECORDING, AND SOME SONGS ARE INTENDED TO BE PUBLIC DOMAIN.

"The mechanical license is paid, according to how many copies will be maufactured and what rate has been agreed to for the license to be issued"
THE RATE FOR A MECHANICAL LICENSE IS NOT "AGREED TO." IF IT IS A MECHANICAL LICENSE, THE RATE IS PRE-SET BY THE COPYRIGHT LAW. HOWEVER, AS STATED ABOVE, THERE IS NOTHING TO PREVENT NEGOTIATING WITH THE AUTHOR/PUBLISHER TO AGREE TO A LOWER RATE (OR TO OUTRIGHT BUY THE SONG)(AND THEREBY MAKE MORE PROFIT FOR THE LABEL)

HOPE THIS HELPS.