For anti personnel use, explosive bullets would limit penetration. When shooting at live targets carrying gear, weapons, backpacks and body armor, you want all the pentration you can get. For any other use, such as anti-vehicle or aircraft, the tiny bullets just don't have the mass needed to penetrate hard objects when the steel/lead core is replaced with the much lighter explosive material. And as pointed out above, you couldn't get enough material in the bullet to be worthwhile.
All of the .30 and .50 caliber "explosive" bullets loaded for military use were intended to be directed against hard targets like vehicles and aircraft, where the resistance at impact is sufficient to detonate the explosive material without a fuse. They were usually an armor piercing/incendiary type of bullet, sometimes combined with a tracer element. They most likely wouldn't detonate against soft tissue, or even bone. Most shells 20mm and above use a mechanical fuse that is too large for the smaller bullets, and must travel a short distance (certain number of revolutions) before it arms.