In the future there will be billions of dollars stored in Wallets, what if one day they decide to stop and shut down their services and transfer all the money to their own wallet and confirm the transactions and convert all of their coins(Bitcoin and any other Altcoins) to USD and disappear?
How can we get our money back? whom can we sue? how can we prove how much coins we had in their wallet?
Well, In case Coinbase or any reputable company tires to scam people, they can do it but that's the only one time profit they will make. Think of a company who took 10 years to develop a repo and they can't think of losing it all for few billion dollars etc. I think Coinbase is very unlikely to do this sort of thing ever.
I agree with you on the reputation part and also this is not only about the reputation since they can go to jail for doing things like that. Basically putting questions like the OP's leads one to living in constant fear and uncertainty. To me this question is similar to "What if all the cops with all their weapons turn into gangsters ?" You can't question everything or otherwise your life might turn to be a total nightmare.