A CX bike is stable, strong, and will take wider tires. It is a great road and commute bicycle. It is built to race in city parks. It has a comfortable riding position. Just put touring tires on it (I like 35mm). I don't mean to advertise a bike but if you look at a high end CX like Moots the even say use as light touring.
You are not going to road race a CX but I will take it as a daily grinder and light touring every time. At the end of CX season in the US and you can usually find great buys on used bikes.
As for risk of injury the only time I would rather be on true road bike is a 50 mph road decent.
But I am 50 years old - I don't 50 mph decents.
This is getting a bit of discussion so will add a little.
I don't road race and gave up my only road bike as for me my CX is was better road bike.
My road bike was limited to 25 mm tires and that is good for racing but not what I want for commuting or even a long road ride. In this pic it has 35 mm tires but with 28 or 32 mm tires it is a road bike. It even came geared more for road (52T). I would not commute on this as it is kind of my baby.
This Salsa below is a bike I bought to CX race but I just did not feel as comfortable on it so I race the above Bianchi. The Bianchi is softer and not as quick. As a commuter and light touring this Salsa is an awesome bike. Other than spend a lot more money on a Moots there is not other commuter I would rather have. I picked this up used for $1600 US. It is light enough to get up and go and strong enough to take a beating and titanium does not rust. And it will take a rack. I also have a steel Salsa Vaya that I use for shopping but even at just a few pounds difference this bike way nicer for light commuting.
I like 35 mm tires for daily commuting.
This is my beater commuter. At my gym I have to leave a bike out in a lower end neighborhood. I picked this up used for $400. For a single speed I like 32 mm tires.
You can do so much with a CX bike. If you get a nice one you will keep it the rest of your life. Avoid an aluminum true race CX bike. A steel bike is heavier but has a longer life than aluminum. Look at the Surly Cross Check. No one races a Cross Check - it is just a ballistic commuter. A bit more money but like the steel Salsa Vaya.