How does the legislative branch hinder the realization of democracy historically and currently?

Well, historically and currently the legislative branch created difficulties for democracy because:

Every 30,000 people in a state = 1 representative who elects the president, as i explained in your last question. So the problem is, the states with bigger population basically have all the power and control the election, pretty much. This is still a problem today (it's also why the senate was created, so each state gets 2 senators = 2 votes).

Historically, states that had a bunch of slaves would count their slaves as a person just so they could get extra representatives. This is why the Great Compromise was made, so 3/5s of the slave population counted as a person.

The Legislative Branch is important because they protect us by making laws. They also manage how we manage we our spending taxes. This branch also affects us in our daily lives.