The answer is, in short, that while such trials did indeed take place, they were not the work of the Turkish Republic at all. To the contrary, the trials took place in a context against which the founders of the Republic defined themselves.

It was the Unionist government that led the Ottoman Empire during the WW1. The Three Pashas (Enver, Talat and Cemal) were prominent figures of the Committee of Union and Progress and it was under them that the Ottoman government legislated forceful relocation of Ottoman Armenians. The Empire signed an armistice in October 1918 and the prominent Unionist figures left the country in November 1918. There were a variety of governments installed, one following the other, after the fall of the CUP. What matters for us here is that, following November 1918, the atmosphere in Istanbul drastically changes. Some even suggest that even Cemal Pasha, one of the more moderate figures in the CUP leadership, was unable to find a single journalist to defend himself in Istanbul newspapers. Surely the whole CUP apparatus did not collapse in a single day. They were forced to remain in silence, however.

The fall of the CUP gave free rein to its nemesis, the Party of Freedom and Accord. Among the variety of things that these chaps accused the CUP of, there was Turkish nationalism. While this party did not always hold power, it and its prominent figure, Damad Ferid Pasha, are important to remember for your question. Another essential thing to remember is that in this period, Mehmed VI Vahdeddin was the new sultan. Equally averse to the CUP, Vahdeddin blamed them and their ways for the downfall of the Empire. He intended to run the country by himself (reportedly telling Rauf Bey [Orbay], a prominent naval officer and future hero of the Turkish War of Independence that the people were like sheep and they required a shepherd, referring to himself). Vahdeddin rightly felt that his sultanate depended on the goodwill of the British, who, after sending soldiers all across the country following the armistice, even invaded Istanbul in March 1920. However, Vahdeddin relied too much on the goodwill and intentions of the British, fearing that the slightest resistance might anger them and lead to an even worse occupation and eventual peace terms. The Treaty of Sevres in August 1920, virtually reducing Turkey into a sort of Central Anatolian Princedom, did not suffice to change his mind.

Understandably, Istanbul under these circumstances became hell for anyone who opposes the Allied occupations, who supported the CUP, or who were even vaguely nationalist. Not only was the political atmosphere such, but Turks of Istanbul also witnessed various 'treacheries' in the form of Turkish women flirting with invading soldiers (which constitutes the subject of Yakup Kadri Karaosmanoglu's novel, Sodom ve Gomore [Sodom and Gomorrah] and similar cases of collaboration which you find virtually anywhere else under occupation at any time. It was also in this Istanbul that the trials you mentioned took place. To what extent were these trials solid, from a legal perspective? While a legal historian can provide a more in-depth answer here (which, of course, is not directly relevant to your question since what matters is why Turks reject these trials rather than how fair they really were), many believed these to be show trials. They involved a variety of motivations harming any legal objectivity necessary for such cases. Some involved in processes were none other than those previously ousted from their positions by the Unionists, older Hamidian officers, and so on. Others hated Unionists for ideological reasons, while still others perhaps hoped that these trials would show the British that these new Ottomans were different from the CUP and deserved to be treated accordingly in peace treaties to come. Zürcher also states that the British themselves wanted some to be tried as war criminals, not only for their roles in the mass murdering of Armenians but also of maltreatment of British prisoners of war (Zürcher, p. 138).

The trials did not last for too long. A new, parallel parliament and government emerged in Ankara under Mustafa Kemal Pasha, involving some minor CUP elements as well. Mind you, Mustafa Kemal was no fan of the CUP, nor was he personally involved in any confrontation with the Armenian or Greek population in the Empire. When the CUP government decided to forcibly relocate Armenians, for instance, he was busy fighting the Allies in Gallipoli. However, this does not mean at all that he was a liberal of sorts. It is useless thinking what he would have done had he been in Enver's shoes. We know he had nothing personal against Armenians (he appointed Agop Dilacar, a Turkish Armenian, as the first head of the new Society for the Turkish Language in 1932), but it does not seem at all that he regretted having bequeathed a more homogenous Turkey. Kemalists opposed the Allied occupation and Greek expansion and fought these with their own forces. With time, they obtained more power, more success, and therefore, more legitimacy. They would eventually win the Turkish War of Independence (1919-23) against the Allies (by then more like Britain+Greece, with France and Italy quickly withdrawing from their Anatolian adventure) and despite the government in Istanbul. As a result, they saw Vahdeddin off in November 1922 (following the successful Turkish Great Offensive against the Greek in August-September 1922). Damad Ferid Pasha was forced to leave the country, with Ali Kemal, a close collaborator of his who happens to be the great grandfather of Prime Minister of the UK Boris Johnson, lynched by an angry mob in November 1922.

When Kemalists established their control, the trials were basically null and void, much as any other legacy of the Istanbul government between November 1918 to September 1922. Indeed, many Kemalists' accounts of the trials show that they considered these to be show trials sometimes led by Kurdish nationalists (Nemrud Mustafa Pasha) and triggered by pro-Allies traitors like Damad Ferid and Ali Kemal. To give you but one example, Kemal Bey, the kaymakam (district governor) of Bogazliyan, was sentenced to death in April 1919, for his alleged participation in the murdering of civilian Armenians. Today, he is considered to be a martyr and a statue of his exists in Bogazliyan.

So, in short, the answer to your question is that the 'Turkish courts' that tried and punished these men did so under very specific conditions. These conditions meant that once the Istanbul government lost any power and credibility it had in the eyes of Turks, the cases too became in effect null and void. Turks considered and still do consider the cases to be show trials that had more to do with pleasing the British and settling old scores with old enemies than with actually confronting the past.

The reference is to Erik J. Zürcher, Turkey: A Modern History, revised edn. (London: I&B Tauris, 2004).