The Constitution doesn’t stop them from requesting or paying for a service, just ordering companies to do it. This is how they are allowed to buy all your location data, and how the cops usually get all your data from social media (no subpoena needed, they just ask), and how it is that crime perpetrators are zapped off social media almost instantly before regular people can look their posts up.
There’s a big, big loophole that people overlook here. FAANG etc have whole departments of people dedicated to voluntarily turning your data over to the state.
On paper, sure. In practice government doesn't really have to worry about government trying to make an example out of them though and has access to the kind of violence and benefit of the doubt evil corporations could only dream of.
Frankly I think it's a bit naive to imply that big government organizations aren't just as evil and terrible and self serving as big corporate ones. Their error bars of evil overlap a lot.
There is also very little consequence for the gov and very little recourse for the citizen in practice. In the event that someone has the resources to challenge the government, any victory is blunted by the award coming from their (and all of our) tax dollars.