Maybe the reason for the large number of cases in the US is people are more mobile in the US. After all, one can travel to 50 states with no border checks. More mobility => faster spread.
The Federal Government cannot restrict citizens from traveling between the states. I don't know anyone, here in the US anyway, who would even suggest such an action.
The privileges and immunities clause, Article IV, Section 2, Clause 1 of the United States Constitution, protects the interstate travel rights of US citizens.
In fact travel rights were actually restricted in practice by the Federal Government and it's agencies, and states under both Republican and Democrat leadership. There are many well established exceptions that restrict access to constitutional rights under various circumstances, so the contention that this can't be done falls a bit flat. If nobody can do it, how come everybody did it?