Is it worth me changing the tyres on my mountain bike?

Yeah. I actually switch between some cheap smooth tires I bought for when I want to commute on my mountain bike (for variety), and the high tread tires it came with for off road riding, when I get a chance to go to a State Park. It's easy and quick just to change them around when you need. This way you won't wear down your high tread (often expensive) tires on the road. If you're not sure how to do it quickly, there are Youtube videos describing the process... some of them designed for speed.