There are lots of problems with speedsters in general:

• they would have to be super strong. This isn't a problem with Superman but would be a problem for Flash. This would also require wearing protection for the eyes since any debris would hit their eyes at massive speeds.
• they would need to take massive amount of calories. Justice League covered this but I'm sure someone can do the math of where the biological organism isn't able to break down food that quickly to get the required calories. This also means that they all would have to be rich to afford this much food and without anyone noticing.
• somehow, their clothes would also have to be indestructible. Again, Justice League somewhat covers this but the new Snyder cut really exposes the problem where the shoes peel off like tissue paper.
• them touching anything while running would more or less explode. This is where the Justice League movie fails. When Flash touches that sword, it would likely go through the entire complex instead of shift slightly.

In your scenario, if Superman used his super speed, he'd kill every single person he touched and - likely - was even next to considering the shockwave. All equipment like doors would be shredded as well. Plus you can't turn easily at high speeds so it's more or less a bullet.

The real problem with the scene as far as Superman in particular is this: Lex is in the Oval Office. There are literally windows behind him. Why not go through the windows instead of the entire building? Since this is Superman, he could have likely fried him from the air from a few miles away.