But why?

To be as direct as possible, the concepts (ideal-types, methodological frameworks, whatever the name) we use to describe historical objects are historical objects in their own right.

The idea of "totalitarianism" as a general XX Century phenomenon - thus going beyond its specific use to describe the social policies of Italian Fascism during the 1930s, the term being employed by the Regime itself - did certainly gain a significant degree of popularity due to its viability as a mean to encompass both WW2 and (especially the early stage of) the Cold War scenario within a single paradygm which pictured the ideals of Western liberalism in direct opposition to an alternative conceit of the State; a conceit, that of the "totalitarian" regimes which was both fundamentally opposed to "liberalism" and, nonetheless, in many regards "novel" and pursuing its own social-economical project and vision of "modernity". It is no surprise that it found a more friendly reception within the "liberal" or "liberal-conservative" field (and, more so, public opinion) than it did within "Marxist" or "Communist" historiography.

Conversely, the tendency to conflate authoritarian regimes and "fascism", ows at least part of its fortune to the attempts to interpret "fascism" as a broader phenomenon than the one traditionally confined to its European and 1919-45 boundaries; the expression no longer of a particular crisis of the European political forms, but rather the product of the impact of new socio-economical models (the ones usually referred to as "Americanism" and "Fordism") onto the growingly interconnected economical system. This interpretation, unsurprisingly, found a certain degree of fortune during the 1970s in the context of (revisionist) Marxist historiography.

Now, while I personally subscribe to a "conservative" interpretation of "fascism" as a phenomenon which is both temporally and geographically defined - that is, a European phenomenon which found its "political" expression only between the two World Wars - and therefore am quite skeptic with regards to any widening of the concept, that's not to say that it can't be profitably adopted to describe other social, political or cultural phenomenons. Yet, I would say that those proposals need to come with a "historical" and methodological reason (as, in the academical field, they ususally do). The fact that a certain "category" exists, does not allow one to use it acritically, as if it was an "inherent" property of the object. Otherwise we run the risk of doing like certain old books, spreading "feudalism", "dukes" and "counts" all over the world's map.

More to your point, the use of "totalitarianism" - some aren't too fond of it, others do still find it serviceable, and others still advocate for its more limited adoption in agreement to its historical contex (that is, as used by the Fascist Regime in Italy) - is inherently meant to address the perceived similarities between two, historically very much opposite, political formations: National Socialism in Germany (and to a lesser degree Italian Fascism) and Stalin's Soviet Regime in Russia and the Federated Republics. Even if we accept it entirely, it plays the same role of the word "pets", which hasn't lead anyone to argue that we should stop calling "cats" "cats" and use "dogs" instead.

Authoritarianism is also generally regarded as a much broader and generic term than "fascism" (even in its broader definition - for instance certain scholars have called either Peron or Videla a "fascist", but most are unlikely to accept the definition for both), and I am unfamiliar with anyone who'd recommend we replace the former with the latter entirely. It is more "descriptive" and somewhat more "neutral" than the more specific adoption of "fascism". One would take no issue with speaking of certain sectors of the Italian radical right (or left) envisioning "authoritarian" solutions during the late XIX Century, but none of those solutions encompassed (all, or most) the traits destined to appear in the Fascist Regime.

You mention the regimes established by Stalin and Mao. Which leads us to another issue: one should, in general, be far more cautious with "exporting" concepts and methodological frameworks than with "importing" them. It's very troublesome to discuss the "general" traits of "fascism" as something which can be applied, summarily, to foreign systems. It makes more sense for a specialist of a certain country/period to "import" some form of "fascism" within their specific framework. I do not see any good reason to claim that Peron, or Videla established a "fascist regime"; yet I can't preemptively dismiss any such argument, unless I am able to address it in its specific historical context and framework. At which point, your question becomes: do specialists of Stalin's or Mao's regimes regard those regimes as "fascists"?

In conclusion, can we broaden our definitions of "left" and "fascism" until they begin to overlap? Yes, but why?

When people advocate for keeping an eye on the "nexus" between concepts and frameworks and their historical relation, they aren't merely being stubborn, but they are advocating for a rather sound approach to history: to regard, first, things that existed and how they existed. That the most prominent fascist regimes went to war with the most prominent "socialist-soviet" regimes is - forgive the overused expression - a "historical fact". Our interpretation of history is subject to change, and embracing "revision" is a fundamental part of any approach to history (otherwise, we'd still be calling everyone and their sister a "count" and a "princess"), but it should come with a sound and sensible reason.

 

For general reference on Fascism, and "fascism", see above others:

Bosworth, R. - Italian Fascism. History, Memory and Representation

Costa Pinto, A. - Rethinking Fascism and Dictatorship in Europe

Costa Pinto, A. - Rethinking the Nature of Fascism

Gentile, E. - Fascism in Italian Historiography - Journal of Contemporary History, (1986)

Gentile, E. - Fascismo. Storia e interpretazione.

Payne, S. G. - A History of Fascism 1914-1945

Paxton, R. - The Anatomy of Fascism