No-one is perfect and no system is perfect. Just wondering what you know that could help us prepare better before moving ahead.
For the traveler, it is a smart service to be used. In my personal trips, it worked out well for various countries. Many of my corporate customers are concerned because of Uber drivers not having a suitable insurance in many countries (solved for US), imposing a risk for the traveler. Due to liability issues and duty of care policies, these customers decided not to activate Uber integration to aviod liability in case of accident. (Thinking model: active integration makes this a service recommended by company. Recommending causes liability.) If the traveler orders an Uber on his own app, it's his personal risk.
If you want offer Uber integration, check per country where your travelers want to use it if conditions like insurance, payment security or data security are sufficient for you.