Should everybody train like an athlete?

No. Let me be a bit more verbose in my answer. Training to be an athlete is predicated on the foundation of a sound level of fitness, which we all can achieve. An athlete trains beyond that in whatever particular discipline, but being fit is crucial. Whether to be a runner, a skier, a power lifter, a cyclist, the list goes on, the foundation of strength, flexibility and cardiovascular endurance is the base on which training to be an athlete, a competitive athlete, is built. It takes time, VERY hard work, and the guidance of a skilled coach/trainer. We can all, with dedication, become fit. To become an athlete is a bit beyond.