Rama did not follow due process in the killing of Vali and exiling his wife. TheThe Shambuka summary execution is in line with the lack of judgement he showed in the two other cases:
https://www.wisdomlib.org/hinduism/book/the-ramayana-of-valmiki/d/doc424848.html
Narada says:
“At this time, in thine empire, a rigid penance is being undertaken by a wretched Shudra, 0 Prince, and this is the cause of the death of that child.
“The practice of unrighteousness, be it in the city or the country, brings about misfortune and the monarch who does not mete out an immediate punishment, goes to hell, of this there is no doubt.
“An act of mortification that is prescribed is well done and a sixth of the merit goes to the king who rules with justice. But how should he, who does not protect his people, enjoy the sixth portion? O Lion among Men, you should investigate the happenings in your kingdom and put down evil wherever it is practised, so righteousness may flourish, man’s life be prolonged and the child be revived.”
Narada has already pronounced a summary death sentence on Sambuka. Rama justified the summary execution of Vali by saying Vali was a monkey - but Sambuka was a human, entitled to due process before being executed.
Sure enough - Rama cut off his head while Sambuka was still speaking
On this that Prince born of Raghu approached the one who had given himself up to rigorous practices and said:—
“Blessed art you, O Ascetic, who art faithful to your vows! From what caste art you sprung, O You who hast grown old in mortification and who art established in heroism. I am interested in this matter, I, Rama, the son of Dasaratha. What purpose hast you in view? Is it heaven or some other object? What boon dost you seek by means of this hard penance? I wish to know what you desirest in performing these austerities, O Ascetic. May prosperity attend you! Art you a brahmin? Art you an invincible Kshatriya? Art you a Vaishya, one of the third caste or art you a Shudra? Answer me truthfully!”
Then the ascetic, who was hanging head downwards, thus questioned by Rama, revealed his origin to that Prince born of Dasaratha, the foremost of kings, and the reason why he was. practising penance.
Hearing the words of Rama of imperishable exploits, that ascetic, his head still hanging downwards, answered:—
“O Rama, I was born of a Shudra alliance and I am performing this rigorous penance in order to acquire the status of a God in this body. I am not telling a lie, O Rama, I wish to attain the Celestial Region. Know that I am a Shudra and my name is Shambuka.”
As he was yet speaking, Raghava, drawing his brilliant and stainless sword from its scabbard, cut off his head.
Even if Sambuka deserved to die, he was not told why he had to die. This was "shock and awe" kind of justice.
