DIY it. Our dryer stopped heating, so I popped the screws off and it turns out the heating coil had burned out. Like $20 on Amazon. Our kitchen sink's faucet cracked and started leaking down the hose into the cabinet below so I bought a new one at Lowe's for like $20. Our oven stopped heating and the clock area where the control circuit is located kept clicking so I gave it a good smack like the primate I am. Free.
Too bad the heating coil wasn’t DRM paired with the dryer, forcing you to have to contact an official repair shop, we could have gouged you for way more than $20.
The examples you gave are much lower in scope than replacing an HVAC.... At various times I have done all of your examples. I do not dare to replace my home's HVAC system.
The "Uber for dogwalkers" service had a problem that people would do an arrangement with the dogwalker outside of its 30% (or whatever) rent-seeking, it even had scary clauses trying to prevent this.
So maybe the solution is to ask the electrician, etc, if you can contact them directly next time, and to ask them if they know any other tradespeople when you need one.
As comment below mentioned, DIY it. While the problem is "PE bad, hurr Durr", what usually happens is veteran plumbing, HVAC, etc businesses with loyal clientele get bought out for a pretty sum by the PE firm. I wouldn't fault them - why would you "work for yourself" when you could just take a nice 7 figure sum and retire or do something else? If your employees don't like it, they can go the same route and start their own thing - which will eventually get bought by PE too.
These are people who never had an exit opportunity before finally finding a way to sell their business for a nice lumpsum, instead of having to live job to job.
The only losers here are the customers and some of the employees, especially those who are undocumented.