Brothers in Unison?

Neither Sugriva wanted to kill Vali nor Vali wanted to kill Sugriva then why did Rama kill Vali?

वालिनो मे महाभाग भय आर्तस्य अभयम् कुरु || ४-५-२३
कर्तुम् अर्हसि काकुत्स्थः भयम् मे न भवेद् यथा |

"Oh, highly fortunate Rama, affirm fearlessness to me from Vali by who I am highly intimidated, and as to how there will be fearlessness to me from him, it will be apt of you to accomplish that, that way... [4-5-23b, 24a]
Thus Sugriva lives it to Rama how he will ensure the fear is removed.
In another Place

तम् अद्य एव प्रियार्थम् मे वैरिणम् भ्रातृ रूपिणम् |
वालिनम् जहि काकुत्स्थ मया बद्धो अयम् अंजलिः || ४-१२-११

"Oh, Rama, today itself you eliminate that enemy of mine in a brother's semblance for my happiness, for which I adjoin my palms in supplication." Thus Sugreeva requested Rama. [4-12-11]
Wrong translation! Jahi is to conquer not kill
Immediately Rama says

उपकार फलम् मित्रम् विदितम् मे महाकपे ||४-५-२५
वालिनम् तम् वधिष्यामि तव भार्य अपहारिणम् |

"A friend is the resultant factor of helpfulness... that I know... oh, great monkey I intend eliminate that Vali, the abductor of your wife... [4-5-25b, 26a]
I intend to kill (वधिष्यामि) says Rama. Hence it is his decision.

Similarly Vali also tells Tara that he will not kill Sugriva but will only thrash him

प्रति योत्स्यामि अहम् गत्वा सुग्रीवम् जहि संभ्रमम् |
दर्पम् च अस्य विनेष्यामि न च प्राणैर् वियोक्ष्यते || ४-१६-७

"You may do away with your perplexity as I will retaliate Sugriva on my going there only to drive him and his arrogance out, but without letting his lives loose. [4-16-7]
So why did Rama kill Vali?

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All Sloka Translations are from the site Valmiki Ramayana