Even beyond the physical benefits of tummy time is the opportunity for brain organization and growth. The more they're on their tummies, the more opportunities to use their limbs, which are making those motions in preparation for crawling - they're not random movements.
Babies are actually DESIGNED to be on their tummies!
Once they figure out that they can move themselves forward using their arms and legs, they not only have a purpose - transportation, getting things - but eventually they develop a cross-pattern, meaning that when the right arm is forward, the left leg is as well, and vice-versa. THIS in turn organizes the lower brain and sets the stage for growth in higher areas of the brain as the baby grows and matures.
Eventually, the baby develops the limb strength for hands-and-knees crawling, and the endurance to to lots of it!
This in turn leads to visual convergence, since the floor is just the right distance from baby's face and the baby's eyes have lots of chances to practice focusing on things on the floor. THIS then leads to the organization of higher areas of the brain.
This isn't about raising a baby Einstein, it's just phases that all babies' brains go through, given the opportunity. On the other hand, lack of these opportunities can lead to shortcomings down the road. Case in point: Josie stood early and cruised early and once she was up she didn't want to go back to hands-and-knees crawling. We didn't know better at the time, so we let her push around a walker from about 8 months on, even though she wasn't walking independently AT ALL yet - didn't happen till she was nearly a year old. She was always a Touchy baby/child, but over time it got worse and worse, and finally we got her evaluated on our own dime - it was pretty comprehensive and our HMO wouldn't cover it. As part of her program, she has to do a lot of crawling - a LOT - but it is helping a LOT. She is less obviously Touchy, and it's impacting her behavior less. She is better-organized, her fine-motor control has made HUGE gains, and she's a lot happier.
With Natalie, we put her on her tummy a LOT, she slept on her tummy, and she's a lot less overwhelmed by things than Josie ever was. It's hard to know how much of that is just a difference in personality and how much is related to how differently we have handled her mobility, and she has her own brain issues - a big-time delay in feeling pain, for example, takes her about FOUR SECONDS to register pain - that we'll have to deal with, but then again, we all have our quirks. I know I have lots of them myself - if only they knew as much about baby brains when I was a baby as they do now!