They are not giving people an educated choice, they are taking that choice away until they deem it okay to give it back. Education is knowing that 7/7,000,000 had a blood clot + the other tests that were done leading up to its release. We know that now. We're educated.
The CVST incidents give a lower bound on risk. The trial data give a rough upper bound on risk (rough due to the small sample size). Knowledge is being refined here. We can't make educated choices without knowledge.
Hard to give people an educated choice without looking into the issue first. Once they know what is going on it will most likely be back to normal. There was a similar issue in Europe, but that neatly overlapped with a delivery shortage of the affected vaccine.
We should give people an educated choice. With unknown side effects we are not doing that. Thank you for pointing that out.
Make sure you cover every possible thing, no matter how unlikely.