Cool idea! I am surprised it's still not working like this. The closest thing I can remember is the Skyscanner. It's primarily a platform for finding flights of all airlines and it does its job pretty well. However, when you choose a flight, it offers you accommodation via Booking and rent-a-car services via the biggest companies in the field.
The reason why things you mentioned, like nannies, private drivers and chefs are not here is probably that people who use Skyscanner usually do not require them. In other words, people who have money pay people to organize trips for them. Travel organization services handle the flights, accommodation, drivers, nannies (or you travel with one - a travel nanny :)), and chefs. It's considered a premium service and costs a lot. If you want a budget driver, nanny, or a chef you call Uber, MeetUp or Uber Eats.
Also, having all the nannies, chefs, and drivers in one place would be a great challenge for one platform since different regulations apply to different jobs. Drivers and nannies require different certificates (or not) and encounter different problems. All of this could be too complicated to handle on one platform.
A great example is Uber Technologies, which got divided into Postmates (deliver anything), Drizzly (alcohol delivery), Careem, Cornershop (grocery delivery), Uber Eats (food delivery), Raiser LCC (legal issues), Uber Freight (logistics), Transplace (managed transportation services), Uber Health (medical transportation), Uber Copter (urban air mobility), Uber, ... Although it was the same firm that owns all of these, it's still impossible to handle everything on one app/platform.