Toyota has behaved in such a manner that it requires oversight in order to continue to do business in this country. When a company shows blatant disregard for complaints which ultimately impact peoples' safety and well being, they require monitoring and need a check and balance system in order to protect the American people.
In any case where defects in a manufactured product have caused injuries or deaths to the country's population, additional oversight is needed. The government is the best candidate to do this, because one of its purposes is to promote social well-being. Three years is enough time for one of the automakers to correct problems in its production processes that have caused unintended harm to consumers, and after that the automaker could be left alone.
In light of the decision regarding Toyota's disregard of complaints of unintended acceleration in Lexus vehicles and consequent issues relative the government does have the right to monitor Toyota for three years to make sure that the work that they are doing is up to par and that those driving them are safe.
No, in light of the decision regarding Toyota's disregard of complaints, the government does not have the right to monitor Toyota, because government monitoring is not the answer to everything. Government monitoring would only make new products and safety measures extremely slow to reach the market. The answer is that someone should sue them.