Except Austrian theory doesn't eliminate these, on the contrary, the Mises-Hayek Business Model Theory states that inflation, deflation, recessions, depressions, etc are all necessary parts of the economic cycle as balancing events.
To expand on your point, Austrian theory points out how the economic cycle is substantially caused by previous ongoing government intervention, and that the contraction phase represents the attempt by the economy to liquidate bad investments and realign itself toward production that is more in line with consumer desires.
So the contraction is as necessary as the boom is artificial.
And the government interecedes, on the basis of political calculus and advice from establishment economists (but I am being redundant); it attempts to spend its way out of the downturn, rather than let the liquidation and reorganization happen on its own. In so doing, it lengthens and deepens the downturn, and lays the groundwork for recurrences of the economic cycle.
Further, because repeated government intervention in the economy builds up the infrastructure for further interventions, and because of the prevailing state-serving mindset of the politico-economic class, future cycles will tend to be more severe than previous ones.
Philospophically, the methodological approach of Austrian economics differs from that of other economic schools of thought, particularly those that are enamored of the idea that their approach should be exactly that of the physical sciences. Mises, Hayek, and others point out that societies, in all aspects economic and otherwise, consists of acting individual human beings. Although one can observe certain basic commonalities across groups of human beings, they remain individuals when viewed at fine scale; and a human is far too complex, and individual interactions in a society far too numerous and complex, to reduce them to meaningful averages on which to make long term predictions.
The unique approach of Austrian economics is that of Methodological Individualism, which explicitly rejects the grafting of the methodology of the physical sciences onto the social ones. This may not turn out to be the comprehensive view that the science of Economics will ultimately need, but it serves at least as a caution to those schools of economic and social thought that become obsessed with quantitative considerations and obscure the acting individuals underneath all that analysis.
Of course, the Austrian approach stands squarely against the predominant intellectual and political trend of the age, which is that of unrestrained, technocratic, intervention in the economy and into the all other private affairs of the citizens of nation. This trend is understandable of one considers the susceptibility of human nature to the blandishments of power and prestige available to those who would serve an all-powerful regime.
It also explains why the Austrian perspective is not widely accepted, although its influence has slowly grown over the years since the passing of Mises, Hayek, and Rothbard.
Perhaps the ultimate contribution of Austrianism is to provide a legacy of thought that will be useful to the creators of some future civilization, to be created sooner or later after the demise of the present one.