To my understanding, thanks to the US's uncomfortably lax privacy laws, immigration officers are allowed to demand you to let them search your phone. If you have fingerprint unlock they can just straight up force you, but if it's a passcode you can refuse. Naturally though if you refuse you're probably not gonna get admitted. Is it at all possible to go back without having a permanent black mark on your record? Eg. paying for your own flight tickets back and going home without a refusal technically there? Or will you have to accept the searching of your phone if you want any chance of coming back to the US (or even any of the other Five Eyes)?
As far as I understand the question, your question is not actually about withdrawing your application, but about not having your phone searched.
It seems to me that you imagine a situation where the CBP officer asks to look at your phone and you say something along the lines of "oh wait, in that case I don't want to get in any more" - and just walk away.
Without trying to figure out the details: This won't work. If they want to search your phone they probably suspect you of something and will not simply let you walk off. Also the behavior itself would be suspicious, and they'd probably enter you into the system regardless of any official ban.
Fortunately, if your goal is to not have your phone searched, there is a very simple solution to that:
Do not bring your phone, or wipe it clean. You can always restore it from a cloud backup, if needed. Alternatively you can bring it and remove all information that you do not want anyone to find.
That said, phone searches are very rare for the average tourist.