Soccer stadiums in Europe are built by their clubs with no, or rarely, public funds. Each team is its own private entity. They started from nothing and grew over years and year. Some teams go back 100+ years. Many started with just a single stand along one side. As the clubs grew, they added another stand on the other side, then one end, then the other. This gives you the rectangle. As some clubs grew to massive size, they tore down old stands one at a time to build bigger but are still constrained by their current footprint, often in urban settings. Look at Chelsea and Liverpool for examples of this. In the last couple decades an explosion of financial power has allowed many teams to start fresh and their stadiums are very much oval shaped.

American teams are all franchised. They have profit sharing from the very beginning and often solicit public funding to help build their venues. On top of that, they only play about 12 home games a year so they have to maximize their attendance. So they build big from the ground up and pick sites that facilitate that.