You don't have to bother carrying a lock (or walk to the corner to find the nearest pole to lock it to for that matter). And, don't tell my Mom, but not fiddling with a helmet and lights is huge too.
Can you imagine going to a car dealership, and coming across a car with 10x the stopping distance and a center of mass twice as high as a Civic and the salesman telling you "it's just as safe so long as you're traveling the same speed and same places"? Would you buy that claim for a second?
I've avoided numerous accidents by being able to stop quickly on my bike, or by making a sharp turn. This varies greatly just between different bicycles -- a mountain bike has much better stopping distance than a road bike. There's obviously also a big difference between a skateboard and a bicycle.
There's also, I think, a steeper learning curve between skateboard and bike, though that may be because learning to bike as a child is more common. There's at least a difference in skill levels. I mostly know the limits of my bike. (e.g., how hard can I turn without skidding out?) and while a skilled skateboarder may be on par with me on that, I'm not. I can bike tens of thousands of miles without falling. I'm nowhere near the skill level of being able to do that on a skateboard.
Being able to eject yourself is also valuable. I suspect a skateboarder would have better "eject and run" options than a cyclist, so that's a point in their favor. (I've had my back tire run over twice, and both times I was able to simply run forward over the handlebars, and my hands (and head) didn't touch the grounds, but it's not always going to be that easy.)
I think the main reason why skateboards are worse injury wise is many of them try to do tricks constantly, while most bicyclists are not in that category. Also the small wheels are more sensitive to potholes.
Surely it's simply because of scenarios like a small rock's ability to insta-stop your board, basically guaranteeing your injury. Pretty much every time I've ever been knocked off a skateboard during my commute would be something you wouldn't even think/care about if you were on a bike. Not even close. One is a bike, the other is a heavy, tall pole (you) on a low, rolling platform. One is far more precarious, like keeping a reverse pendulum balanced.
Hell, the most common injury I've seen on a skateboard is just someone stepping onto one, misplacing their center of mass, and the board just rocketing out from under them, and then bruising their tailbone/wrists. Even an inexperienced bicyclist doesn't have a fail case close to that.
This gets more true the further you are from sprinting on a regular basis. And really unless you have practice you're not going to match speeds with the ground anyway
If you did then you're probbably faster than normal and better balance than normal. I'm pretty sure I'd pull a hammy immediately. My coworker immediately face planted and broke arm and collar bone.