Of couse the problems you outline transcend state boundaries. However, finding the solutions to these problems was delegated to the states and not the federal government.
Yes, Jefferson referred to our system as a "Democratic Republic" as well as Madison's description. The reason being that in a large area it is not possible for the average citizen to be well enough educated on all the issues and circumstances for every area to make well informed decisions while perfoming their daily tasks.
There are multiple solutions to each problem, but not one solution works well for every area. The role of federal government is not to solve these problems with mandates handed down to the states, it is to ensure that the solutions chosen by the people for their states are Constitutional. The simple majority can't rip away the rights of the minority because they have more votes.
Regulation is necessary, but it needs to be in the right tone. That of restriction not mandate. Insurance companies, banks, etc.. can't do A,B,C. Saying that someone can't be discriminated against based on race, gender, age, etc... is not the same as saying a certain percent of business done needs to be done with people of these demographics.