I think the point of view here is off, the CPU is the thing that is being used, it's not the thing doing the using.
So you run a game, the game is the thing doing the using, in this case it's using the CPU. The game will use up as much of the CPU as its design demands. If it is a new game designed to use a lot of CPU performance, it will keep loading the CPU until one of two things happens. One, it gets as much CPU performance as it needs, so it does not demand more. Or two, it reaches the maximum the CPU has to offer. So that's when lag happens, as the CPU needs time to catch up to the demands being placed it.
"ie: will a faster clock speed reduce a CPU from reaching high utilization so often?"
The clockspeed is only one possible way of determining CPU performance. Just as important is the software you are running. Not all software is equally demanding. A low clockspeed multi-thread CPU might perform excellently on software that uses those threads, while a very high clockspeed single core single thread CPU may perform poorly on that same software.
As far as reducing utilization, you do that by selecting the correct components for your needs. This is why people always ask "What games are you going to play?" when answering questions about GPU or CPU advice. There is no single CPU that is the 'best' since what's best for you might not be what's best for me. Once you identify what you'll do with it, then it's possible to choose what's best for that particular purpose.