Colin the 70-300 is capable. All lenses have their limits, just with some the limits are fewer. The “lack” of sharpness can be any number of things from optics, to camera settings, cropping if you are, to practise in software editting.
That said with wildlife and simliar you do want to think about getting a lens thats designed for it. The 70-300 is sort of an all purpose lens designed for mass consumption. Its a good place to start and get your feet wet, but people who really want to do some wildlife stuff will upgrade from. There are all kinds of options for almost every budget.