The reason for that has nothing to do with dangers of vaccines, but is a policy designed to keep vaccines available without subjecting pharmaceutical companies to costly lawsuits every time a kid happens to get sick or injured at about the same time as they received a vaccine. The profit margin on vaccines is so thin that it does not take many such lawsuits to make vaccine manufacture and sale a costly liability for the company. That is true even if not a single lawsuit has any factual basis.
It is a sad fact that people will sue for any bad medical outcome, regardless of whether any human action could have made the outcome any different. And juries, not understanding science or cause and effect, feel sorry for them and award them huge damage awards. You know that lawyers are out trolling for clients--I see their ads on TV all the time: "Have you ever used this drug? Did you suffered any of these side effects: psoriasis, heartburn, blood clots? Well, Shyster, Swindler, and Golddigger are here to help! Call us at 1-800-GET-RICH and we'll get the big payout that you deserve!"
Given this environment, it is inconceivable that any company would try to market a product that is even the slightest bit unsafe or whose benefits drastically outweigh its risks. Heck, even after companies have invested hundreds of millions into a drug, they will still pull it after adverse events--even if those adverse events cannot be directly tied to the drug.
The reason for that has nothing to do with dangers of vaccines, but is a policy designed to keep vaccines available without subjecting pharmaceutical companies to costly lawsuits every time a kid happens to get sick or injured at about the same time as they received a vaccine. The profit margin on vaccines is so thin that it does not take many such lawsuits to make vaccine manufacture and sale a costly liability for the company. That is true even if not a single lawsuit has any factual basis.