The real reasons are more complex. Metallic uranium occurs naturally in tiny quantities. It is a poisonous heavy metal like lead or mercury, but only slightly radioactive. In Wonderland world of high-energy collisions. When metal meets metal at five times the speed of sound, hardened steel shatters like glass.
Metal flows like putty, or simply vaporises.
A faster shell does not necessarily go through more armour, but, like a pebble thrown into a pond, it makes a bigger splash. Armour penetration is increased by concentrating the force of a shell into as small an area as possible, so the projectiles tend to look like giant darts. The denser the projectile, the harder the impact for a given size. DU is almost twice as dense as lead, making it highly suitable. The other metal used for anti-tank rounds is tungsten, which is also very hard and dense.