Peter made incredibly broad-ranging changes to Russian society: he changed the relationship between peasants and the gentry, he (rather forcibly, at times) changed the very style of dress of the gentry, he brought Russia's aristocratic wives from seclusion to Court, and he made wide-ranging orthographic reforms.
But when he did the latter, why didn't this Emperor - so well-traveled across Europe and so fascinated with Europe - go further than merely implementing huge orthographic reforms to the Russian language and implement the Latin alphabet?
Peter's orthographic reforms began in the early 18th century as Russia moved towards Europe. In the early 20th century, in Turkey, Ataturk abolished the Arabic alphabet in favour of the Latin in his attempt to Europeanise Turkey.
It seems curious to me that an Emperor so obsessed with Europe to the extent of repudiating almost all of his cultural heritage wouldn't adopt the Latin alphabet, particularly given his immense power over the very few of his subjects who were literate.
It's always harder to answer why something did not happen, than why and how something did happen.
Now, I am no expert on the Petrine revolution, and I do not know whether adopting the Latin alphabet was specifically considered, or if there exists any explicit reason for it not happening. (I suspect this is covered in Abram Shitsgal's 1959 Russkiy Grazhdanskiy Shrift 1708-1958, which I do not have on hand.) But there are some clues to the general thought behind the Latinisation of the Cyrillic aphabet, which may offer some insight.
During the first decades of the 18th century, printing of books in Russia skyrocketed, so did the number of non-religious books: from a negligible number to 75% of all publications. This is why a new alphabet, more suited to print than the complex Old Church Slavonic script (based on Greek and developed through centuries of hand writing), was needed.
During the years 1698--1708, Peter personally comissioned Dutch printers to develop suggestions. After personally revieweing each letter and finally inviting the printers to Moscow, he arrived at what was called the Grazhdanka, or the "civil" Cyrillic script, more or less the one used today. These were, as is still evident, based on Latin printed typefaces.
So why did he not simply adopt the Latin alphabet?
We can find a clue by looking at the linguistic reforms that were not orthographic. In the wake of an enormous technical and scientific revolution, a vast new lexicon was introduced to the Russian language. And hand in hand with the "civil Cyrillic", Peter encouraged texts written in a prostoi, or simple, style. This meant the archaic and clerical language was switched for a vernacular accessible to military personnel, bureaucrats, craftsmen and students. In short: he wanted to expand the literate classes, allowing his ideas to gain traction.
This strongly points towards an effort to draw Russia and the Russian language closer to Europe, but also to facilitate a shift rather than to upheave the status quo for the sake of marking a shift.
Atatürk wanted a swift and clean break with Ottoman culture, going so far as to ridicule traditional dress and customs. Peter sought a modernisation of his country's technical and educational standards, but not necessarily at the expense of purely symbolic changes.
Because implementing Latin script would have a drawback: it would slow the process of adapting the new sciences and techniques that were ultimately more important to Peter.
Some scholars, among them Ivan Iliev, also claim that
The reform was a compromise between the supporters of the old Cyrillic tradition and the supporters of West-European culture.
Sources mention the Church advocating the continued use of Old Slavonic script, and some after-the-fact criticism of the Gradzhansky letters, but none of these were politically potent factors. Everything I have read points to Peter himself making the final decision to reform rather than replace the Cyrillic alphabet. So I would assume that was in accordance with his greater plan, to facilitate a spread of literacy and enlightenment through making an already understood script easier to both learn, read and disseminate.
To me, this has similarities with Nazi Germany's abolishment of the traditional Blackletter script in 1941. They claimed it was because of "Jewsih influence". In reality, it was because most people in occupied areas could not read it. Using Antiqua was just simpler.
TL;DR: While ideology was important to Peter's modernisation of Russia, in this case it seems he prioritised practicality.
Sources:
-Bennett, Brian. Religion and Language in Post-Soviet Russia. Routledge, 2011.
-Cracraft, James. The Revolution of Peter the Great. Harvard University Press, 2009.
-Iliev, Ivan. Short History of the Cyrillic alphabet. In: "International Journal of Russian Studies", no. 2/2013.
-Kamusella, T. The Politics of Language and Nationalism in Modern Central Europe. Springer, 2008.
