The provocative answer-to-the-question-with-a-question is, “What new order?”
While a new constitution was promulgated in 1946, the new Italian Republic looked suspiciously like the old Italian Kingdom once you got over the fact that the President of the Republic replaced the monarch and that elections replaced appointments to the Senate (the upper chamber of parliament). While the new constitution made new overtures to inclusiveness and enshrined new liberties (women could vote!) much of the ordinary apparatus of government remained the same. I examined how much of Italy’s fascist-sympathizing underbelly remained untouched even if as the dictatorship’s leaders were removed in this answer from a few years agowhich might interest you. Although I'll also add that for the purposes of this answer it’d be disingenuous to not acknowledge that within the wider narrative of continuity, once freed from the shackles of dictatorship new meritocratic opportunities did emerge both in public and private sector (“The change in the managerial class and the ordering of the state is radical […] in spite of the persisting lines of continuity with fascism, both in the medium-high tiers of the bureaucracy both of economic institutions and legal institutions” writes Emanuele Felice. If we’d like, we can summarize the process as individual episodes of renewal within a broader line of continuity).
But even in a climate of more-continuity-than-we’re-letting-on, it's true that the IRI’s survival in Republican Italy was far from certain: Its establishment and growth had only ever been meant to provide a suite of temporary solutions, first meant to mollify the effects of the global economic depression of the 1930s, and later the institute was found to be a useful instrument to mobilize the economy for war. But the fascists didn’t have plan for long-term state involvement in the capital (or management) of industry, and had never led on that they considered developing one. The IRI had also been primarily thought of an institution favoring import-substitution, as Fascist Italy had barred its borders to foreign goods and the IRI had been tasked with developing domestic industry to bridge the gap. But now, the leadership of Republican Italy worked hard to integrate itself in the globalized economic system led by the United States, further favoring the IRI’s obsolesce.
Inertia, in great part, contributed to the survival of many fascist-era institutions in the early Republican era. But a major contributing factor to that inertia was also the impact of the war, defeat, military occupation, and destructive civil conflict. Continuity was easy because it was pragmatic, and in the IRI’s case, the inevitably pragmatic question is that if it were to be liquidated who would buy the shares it owned? Not Italian families, whose savings had been depleted by war and inflation. The entrepreneurial class was still licking its wounds too, busy with consolidating what little capital they had preserved. Credit markets had collapsed and needed to be reconstructed. Could foreign capital have stepped in? Not just yet to the extent it would have needed to: this was still an era (although not for long) when entrepreneurs often had to physically relocate to oversee new capital investments (as an example, as late as the 1950s when Nelson Rockefeller invested in a chain of Italian Supermarkets the operation required periodic in-person meetings in Italy, transplanting American representatives and executives to Italy, and Rockefeller ended up selling his stake in the venture by 1961).
The IRI also had company: it wasn’t the only economic institution in the hands of the Italian government. State-owned enterprises active in various segments of the oil and gas sector had also been instituted by the fascists starting in the 1920s (predating IRI) and in the 1953 were rounded up in a unified conglomerate: ENI. Even given this, state intervention in the economy was never perceived as a particularly fascist idea: in the late 40s plans were drawn up for a development bank meant to bridge the financing gap for public works in the south of Italy, and the institutions set up during Roosevelt’s New Deal were cited as inspiration (although the The International Bank for Reconstruction and Development (IBRD) and International Monetary Fund (IMF) were also probably significant influences). Italy’s national development bank, the “Cassia del Mezzogiorno,” was founded by law in 1950.
Lastly, the IRI benefitted from performance legitimacy. Sure, decision makers choosing not to dismantle it in the late 1940s couldn’t have known it, and it’s true that in later decades the IRI would contribute to muddying the line between the Italian state and the country’s industrial system (creating conflicts of interest and diluting responsibilities). But early in the 1940s and 1950s the IRI’s companies quickly established themselves as drivers of the country’s growth rate which consistently outmatched that of the rest of Europe for nearly three decades. By the 1950s, the IRI had established itself as a central component of the country’s economic system, and its companies were major contributors to the Italian standard of living growing to match the rest of the west by the 1960s. It remained, in other words, too ingrained to the country’s economic performance to do away with.