If you're sticking to destinations on the main roads you should be fine with a rental. Your costs may not be hugely lower but you can control your own itinerary and stops (although there's also something to be said about not having to drive 12 hours or more yourself and the creature comforts of a bus or van). Some locations can only be reached by 4x4 "super jeep" which might make your vehicle rental costs too high to be pratical. I'd also be cautious about going offroad on your own without backup since like Alaska the wilderness is very unforgiving and dangerous to the unprepared. But yes you can do most things without tour groups but they do afford you a certain amount of luxury (e.g. not having to worry about the PITA to manually deflate and reinflate tires when crossing streams or rocky terrain, etc.)
Long story short, figure out what you want to do first and then decide if a tour group is the right way to do it. Some times doing it yourself might be better, other times a tour group will be a good deal, and sometimes you'll have no choice (like if you want to go dogsledding you're obviously not going to do it yourself).