One of the misconceptions that people have about traffic law is that it is illegal to change lanes in an intersection. Quite often, it isn't. (Check what the law actually says in your state). One of the laws here in Arizona requires that a driver not pass another vehicle (left of the center line) either within 100 feet of an intersection, or while passing through one. Over the years, people started remembering this as a prohibition on changing lanes, rather than crossing the center line. These are two separate things.
At 3:00 a.m. on a deserted city boulevard, it may not be unsafe to change lanes in an intersection. But one of the elements of safe driving, and driving in compliance with law, is that we make a habit of doing the "right" thing. Here's an example. In my state, you must signal a turn at least 100 feet in advance. But there is an exception; if no one else is nearby that would be affected by the movement, you need not signal. If you think about this, however, it is better to always signal the turn, making it a habit rather than trying to decide in each instance whether anyone will be affected by the turn. If you practice the latter approach, eventually you will make a mistake; you won't see someone coming and NOT signal a turn you should have. You may cause a collision, or get a citation for failing to signal. So, we say ALWAYS signal, and it will be more likely you WILL signal when it is necessary for safety and legally required.
For the same reasons in reverse, you should make a habit of NOT changing lanes in intersections. Think about all the potential conflicts and the possible high speeds of traffic approaching and transiting intersections (remember the average speed of traffic through a controlled intersection is about 52 miles per hour). Think about everything that is going on out there -- turns, red light runners, people heading toward you that may be distracted by internal or external factors, pedestrians. Why add another complicating factor to that mix? It may not be illegal to change lanes in intersections, but perhaps it should be. Practice holding your position relative to other traffic and staying in the same lane until you are safely through. Make it a HABIT. Also remember to slow down before entering the intersection to give yourself extra space and time.