Where are the good dogs?

I agree with the others. A higher rate seems to weed out the dogs (and owners) with bad behavior. Also being explicit in your profile about which behaviors are dealbreakers for you (I live in an apartment so I cannot take large or constantly barking dogs, I have a roommate so the dog must get along with people, etc).

And a meet & greet is mandatory for me. Mine last about 30 minutes and I observe the dog as they exit the vehicle, as they approach the house, while they are in my house (living room, dining room area only) and while they are in the back yard. I have a list of questions for the owner regarding behaviors.

So far I have had nothing but great clients. I'm in the middle or above range for sitters in my area, and I have never gotten a dog with behavior problems. This is not to say that I won't or that my rate is the deciding factor, but people who value and train their dogs seem to be willing to pay more for someone to keep their dog (or visit or house sit).

I can't see where you are or what your rates are.

For whatever it's worth, I've found that pet owners willing to pay higher rates, have better trained, healthier, nice temperament good dogs. Another nearby sitter who I know very well, who has helped many non-rover (i.e. CL) people out, accepted about half of the competitive market rate in our area, and every time has dealt with major destruction, training, behavioral issues, etc. Usually, she skips doing m&g (for rover too) and often ends up with barkers, etc. Although I agree the m&g isn't always an accurate predictor, I've found it helps.

If you live in a low income area and/or charge lower rates then you'll probably get more behaviorally challenged dogs. I don't know where you live; I've experienced a few difficult dogs but nothing as consistently destructive as you've described. Maybe you need to raise your rates and always be sure to do a meet-n-greet first. Make sure you feel comfortable with the owners and the dogs before booking the stay because you can usually gauge some problems at a meet n greet. If the owner doesn't want to do a meet n greet it might be a good idea to pass on them. You will probably have to take on less dog clients but they will be better quality stays

Always do a meet and greet. I will not take a dog without it. You will pick up on the way dogs with anxiety pace and look around your space. I have had a couple of dogs with separation anxiety and Never Again! I have learned my lesson. Hindsight is 2020.
-ask if the dog can be left home alone and for how long. -ask if the dog barks when left home alone.
-ask where the dog sleeps just a few options. Hope it helps.

Also, I never take more than one dog. For me you just never know how other dogs will be with each other. You will notice usually within a few minutes if they will get along or Not.