the people you pay to do it aren't going to do it any safer than you would and if they get hurt you're liable. You may as well watch some youtube, take your time, and do it yourself.
That is about as true as you being liable for a mechanic hurting themselves working on your car or a repairman falling off the roof fixing your HVAC in that it's not true at all.
Now, if a mechanic is working on my car and my garage door spring snaps and injures them then yes, I would be liable.
Separately, being liable for something happening to someone else and that same thing happening to me are not equivalent. Macabre as it is, I'd rather pay out (or have my insurance pay) the lawsuit for a professional hired for a particular task ending up grievously injured than end up grievously injured myself. In a lot of cases, I'd doubt you'd even be financially liable. From a moral standpoint there's still some culpability, but in the case of garage springs I think your obligation is more to stress to the professional that you're happy for them to take their time and you're willing to pay accordingly than it is to subject yourself to the risk instead. From a societal standpoint, a few repairpeople building up expertise at a particular task is safer than everyone doing it individually.
Averagely experienced woodworkers loose fingers most often.
When you are new to something you are super careful. When you are veteran you made or seen somebody make all mistakes already.
When you are averagely experienced it's the most likely time for your confidence to exceed your capability.
Don't hire that person. Hire someone with insurance. You as homeowner are really unlikely to incur any liability as long as you are not substantially directing their work. Let them be the expert doing their job.
There are times to make repairs yourself - such as when you think you can do a better / more nuanced job than a "pro" or when acquiring the skill can pay dividends over a long period (eg once you learn to change your oil and rotate your tires, you will have the option to never pay for it.)
Taking on the injury instead of letting a pro handle is is explicitly NOT the reason to DIY! Presumably the pro has done that thing many times and survived, and even if he fucks up that's the risk of his job.