In the US, the Constitution lays out a division of responsibility between the branches. The Constitution grants certain powers to each branch. All the members of all the branches represent the people through different mechanisms. Interpreting the law, including the Constitution, is the job of the judicial branch. If a question of changing the law comes up, that goes to the legislature. If a question of interpreting the law comes up, that goes to the judicial branch.
We have a representative democracy, not a direct democracy. Direct democracy doesn't work very well at all. States that implement ballot measures usually come to regret it. For example, if you put a proposition on the ballot asking voters if they want to spend $10 million on a new rail station, just about exactly the same number of people will support it as if you put it on there with a $10 billion pricetag. People just don't have the time to sit and work through all the policy details. It works much better to have the people pick representatives and have them learn all the details on the people's behalf.
Another problem direct democracy states tend to run into is voters requiring them to spend a ton on various things, requiring them to keep taxes low and then denying them the ability to borrow. So, you end up in this weird situation where the legislature has no choice but to slash core services while being required to keep spending on whatever frivolous things, and keep the tax rates that the ballot measures addressed low and make up for it with whatever avenues are available, like setting super high DMV fees or whatnot to balance the books... Policy details just isn't the kind of thing a person can intuit the correct answer to in 15 minutes a year sitting on their couch. It's the kind of thing you want teams of accountants and analysts and whatnot pouring over for years.
The idea that representative democracy works better isn't just my personal opinion, that's one of the core ideas the nation was founded on and it has worked out quite well. Direct democracy has sometimes worked out ok, but generally only at a very small scale. Representative democracy has a far better track record.