You can certainly use a Dutch oven (DO) for cooking sauce. A good DO is probably one of the most versatile pieces of equipment in the kitchen. It cooks, it bakes, it even fries! It will certainly make sauce and the high sides will even help prevent splatters. I wouldn't worry about the lack of a long handle, the weight of the DO will keep it stable.
If anything, the weight is its primary fault. A good DO is also a heavy DO. It can be a bit daunting to lug out every time.
Since you mentioned Le Creuset, I'm assuming you're talking about enameled cast iron - not 'normal' cast iron. And hence haven't addressed that you certain sauces and such may not be well suited to 'normal' cast iron, but enameled is fine all around.
Can you use a enameled Dutch oven for sauces? Absolutely. Should you? There are less weighty options, but at the end of the day it will make the same sauce.