Yugoslavia had very real tensions. Whether the breakup was inevitable is harder to say, however. It was structurally unstable, but the economic crisis of the early 1990s, a simultaneous constitutional crisis, the rise of nationalists, and the breakup of the USSR all played a role.
One thing to keep in mind is that constitutional structures were a real impediment. The Yugoslav constitution was already highly decentralized, and it made it difficult for any central government to coordinate or act. Ante Markovic, the last pre-breakup president of Yugoslavia (and a Croat) was extremely popular throughout the entire country early in his tenure, but his reforms stalled when blocked by the Serb and other republican governments. While Yugoslavia needed a real federal system, there needed to be a more effective federal government and national elections.
This btw is not unrelated to the Soviet-style structure of the state. It's telling that for all the balkanization tropes in Alternative History, the only modern post-WWI examples are the three major Communist federations: the USSR, Czechoslovakia, and Yugoslavia, all of which were on paper extremely loose confederations which invested a lot of sovereignty (and even the right to secede) in their constituent republics but were held together by centralized party bureaucracies.
One additional factor in the breakup was the Soviet Union's breakup. Soviet collapse, for a number of reasons, encouraged European and Western governments to back secessionist regimes. A surviving USSR would almost certainly have opposed recognition of Slovene and Croat independence, and would likely have prevented European governments (primarily Germany) from supporting them. This might have led to a negotiated outcome in 1991, perhaps with a similar structure to the later State Union of Serbia and Montenegro. Obviously, given what I said above, this would not have been an ideal solution for Yugoslavia, but it may have held it together long enough to get through the early 1990s crisis, and if it had been included in EU enlargement in the late 1990s or early 2000s, it's unlikely a full breakup would have occurred (though secessionists would likely still be a major factor, similar to Catalonia or Scotland).
It's also worth pointing out that even today, the majority of the public in most of the former Yugoslav republics regret Yugoslavia's breakup, the exceptions being Kosovo and (admittedly major) Croatia. Even in Slovenia, the figure regretting the breakup is surprisingly high.
One thing to keep in mind is that constitutional structures were a real impediment. The Yugoslav constitution was already highly decentralized, and it made it difficult for any central government to coordinate or act. Ante Markovic, the last pre-breakup president of Yugoslavia (and a Croat) was extremely popular throughout the entire country early in his tenure, but his reforms stalled when blocked by the Serb and other republican governments. While Yugoslavia needed a real federal system, there needed to be a more effective federal government and national elections.
This btw is not unrelated to the Soviet-style structure of the state. It's telling that for all the balkanization tropes in Alternative History, the only modern post-WWI examples are the three major Communist federations: the USSR, Czechoslovakia, and Yugoslavia, all of which were on paper extremely loose confederations which invested a lot of sovereignty (and even the right to secede) in their constituent republics but were held together by centralized party bureaucracies.
One additional factor in the breakup was the Soviet Union's breakup. Soviet collapse, for a number of reasons, encouraged European and Western governments to back secessionist regimes. A surviving USSR would almost certainly have opposed recognition of Slovene and Croat independence, and would likely have prevented European governments (primarily Germany) from supporting them. This might have led to a negotiated outcome in 1991, perhaps with a similar structure to the later State Union of Serbia and Montenegro. Obviously, given what I said above, this would not have been an ideal solution for Yugoslavia, but it may have held it together long enough to get through the early 1990s crisis, and if it had been included in EU enlargement in the late 1990s or early 2000s, it's unlikely a full breakup would have occurred (though secessionists would likely still be a major factor, similar to Catalonia or Scotland).
It's also worth pointing out that even today, the majority of the public in most of the former Yugoslav republics regret Yugoslavia's breakup, the exceptions being Kosovo and (admittedly major) Croatia. Even in Slovenia, the figure regretting the breakup is surprisingly high.
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