Most professional photographers will have a back up plan in place in case of illness, emergencies etc with an associate photographer who is similar in shooting style.
Hitched said in their article: People get ill and family emergencies happen. Your photographer will likely have a network of fellow professionals they can call upon if circumstances change unexpectedly. Despite the best laid plans, it’s always recommended you get wedding insurance to cover for any last-minute disasters. Listen to your gut if they ignore the question – you’re only going to have one chance at this day and you need to trust they have you covered.
Which is definitely good advice on this subject as for sure you don't want that stress on your wedding day, however, insurance will only help for afterwards, and sometimes not at all. There was a photographer recently who went out of business and left hundreds of couples without a photographer or videographer for their big day. Because he was scamming people, there was no official liquidation papers to give to the couples so the insurance wouldn't pay out. So not only did they have the stress of trying to find someone new, sometimes days before their big day, they also were out of pocket.
Another supplier I know recommends putting aside contingency money in case of emergencies with suppliers which is great advice, and from my side I'd ask your photographer if they have a backup plan in case of emergency. For me, I have a network of photographers who'd be able to help if I couldn't do a day, and I'd have to be pretty much dead not to shoot a wedding.