The phrase "the purpose for" is correct and usable in written English.
You can use this phrase to refer to the reason something is done or exists. For example: "The purpose for the meeting is to discuss the new budget."
"The purpose for us is very simple.
I think that was the purpose for using them.
"The purpose for government is not grand but simple.
So the purpose for me was to articulate how important Versus was in fashion history".
The purpose for which ethical auditors are generally employed is to find nothing.
Emma Hunt: "It depends on the purpose for your work Twitter.
–What is the purpose for the editorial section of a newspaper?
This is the purpose for the periodic review of detention status provided for by the regulations.
And that's what completely negates and vitiates the purpose for such an amendment".
Only during Wilson's tenure has the President's Room served the purpose for which it was designed.
On the blank where it says: "State the purpose for which this loan is to be used," he put down.
