Mori had all sorts of ideas for reforming Japanese society. But to understand the context of his idea, you really need to understand the state of the Japanese language in the immediate aftermath of the Meiji Restoration. Specifically, that it only kind of existed.

Let's take a look at a word most westerners will be familiar with: samurai (侍). So, simple question: What was a samurai? That depended on the realm, meaning there were literally 265 definitions. (More, actually.) There were a number of points of cleavage. Did a samurai need to receive a stipend? Did they need to be descended from samurai? Did they need to serve in a military capacity? Did they need to serve the daimyo directly? What about the ashigaru class, which was another (sometimes) hereditary class of (sometimes) stipended warriors. Were they also samurai or did being an ashigaru preclude you from being a samurai?

"Uh, you know what. Easy answer. Nobody. Nobody's a samurai." -Japan, 1869

And I am not biasing that result by choosing a politically contentious issue. Different words were used for the same object in different parts of the country. One of the few nationalized vocabularies was that of farming capacity and taxes because the Tokugawa enforced that. However, even to achieve this the Tokugawa had to resort to expediencies like just declaring certain arbitrary conversion rates or amounts. (The Daimyo of Hokkaido, for example, was arbitrarily set at the minimum limit of 10,000 koku.) And you still had things like whether koku rice had to be processed before being measured or not, such that domain's kokus had different effective worths. (And this isn't even getting into minority languages or their hybridization with Japanese.)

Alright, so we've agreed that there's such a thing as a samurai. And we're fortunate enough that everyone tries to use the same word! (As opposed to what you call fish. But that's okay: it's not like the Japanese eat a lot of fish.) Great. That word. How do you pronounce it? How do you write it?

You had everything from minor variations ("saburai") to people who used "shi". There were multiple ways to write it too, again from subtle variations to people still using Classical Chinese. (And again, we are ignoring minority languages and Japanese who borrowed words from them.)

"Uh, you know what. Easy answer. Nobody speaks Japanese anymore." -Mori Arinori, 1886

I'm joking. But Mori's project was not so much to create a system to impart a national language but to create one from a patchwork of dialects. As a radical westernizer, simply teaching everyone English as a national language and letting them keep their local dialects had an appeal to Mori. In his view, it would benefit Japan by making it more able to trade, learn from, and communicate with the most powerful nations in the world. It would smooth over contentious regional issues. And, importantly, it meant he had a pre-existing language that was complete and uniform already. The idea was not to eliminate Japanese as a language but to make it Japan's language of education (and subsequently business, science, etc).

So was it a realistic prospect? Not really. The idea isn't as strange as it might seem but foreign influence was a contentious issue in Japan. Further, Mori was already suspect for being a westernizer and a member of a minority religion. (In fact, this was part of why he was assassinated: the ultra-nationalist felt he had betrayed Japanese religion and disrespected a Japanese temple.) It would also have been at odds with the government's program of national patriotism through schooling.

Mori (and the Japanese government) instead embarked on a program that would be familiar to those who've studied German or Italian. They basically made High Japanese (though they never used such a term): a Japanese that was officially sanctioned and taught. This is still done today, with the government adding or subtracting characters and putting out official rules on what the language is.

From Mori Arinori, A History of the Japanese Language, Japanese Dialect Ideology From Meiji To Present, and War and State Building in Medieval Japan.