Our deer are a hazard, and so the DNR encourages us to thin them out. They cause accidents, destroy crops, and so on. As such, we have what is called the bonus doe program. Under this program you can buy additional tags to get as many doe as you want. Each county has a limit on how many doe you can shoot. In my county, you can take 8 doe per season, in the next county north you can take 4.
However, you are only allowed to take one buck per season.

here is a pic of my bow, not finished in this pic -it doesn't have the antler on it.

I have never used artificial sinew. As I understand it, it is just fiberglass. I have used fiberglass strips for a backing before. Sinew is worlds above fiberglass, but very difficult to use. It takes a lot of work to prepare the stuff, and it is hard to get it on right. You can only put it on with hide glue, and the stuff sets up in 1 minute after taking it out of the hot pot. not much time to get things right! But the results can't be beat.
This is the only type of traditional bow I know of that can outlive its maker. A regular wood bow wears out over time, but these ones just rely on wood to serve as the support for the other stuff, so it doesn't matter so much. Sinew and horn/antler will last forever if kept dry.
The big disadvantage of a composite bow is that it looses strength in humid conditions. But when the temperature is below freezing, or close to it, then that doesn't really matter.