On the other hand, I wish it were a more formalized process rather than this politicized "our president made a deal to save america!" / "Intel is back and the government is investing BUY INTEL SHARES" media event. These things should follow a strict set of rules and processes so investors and companies know what to expect. These kind of deals should be boring, not a media event.
Government benefits through one, generating employment - direct and indirect employment, raising taxes through personal taxes (indirectly impacting tax collection) or second the country being at the forefront of the innovation etc. That is how average tax payer was supposed to benefit.
But I guess trying to nationalize companies and "benefiting" from company profits was something people were missing. How did no one see that? Ah yes, third world countries try this routinely for "national security" and it always leads to moral hazard pointed out by the person above you.