A company doesn't need to be owned by the govenrment (which I assume is what you mean) for the government to guarantee it is free from being bought out by it's competitors. Whatsapp/Instagram were great examples of this - where the leader in a sector managed to buy its primary competition. As far as I understand it no one can credibly claim Instagram's growth has been prioritized relative to Facebook - why? Becuase Facebook prioritizes facebook.
This isn't a question of "will the economy collapse if X buys Y" it's a question of "Which will yeild the best outcome, Y being acquired by X or no". The exact definition of "best outcome" is where the entire battleground though.
It is quite difficult to see who actually could acquire ARM though - because of ARM's quite unique position, any of the potential acquirers are either customers (Apple, Nvidia, Qualcomm) who would be vertically integrated to beat out competitors or direct competitors (AMD, Intel). I think almost the only people who could buy ARM at this point would be TSMC.