Wrong! Everything we build is on top of layers upon layers and not a single company/IT team has/can fully control all of them! So you suggest: build your own backend API and run it on a VPS/Container/whatever. Do you have full control on the hardware? The virtual machines? The vendor's infrastructure? Let's move a layer up. Do you have full control over the framework you used? The database engine? Does the sum of knowledge/experience in your team guarantees full control on all these layers? Under a security threat who provides the patches? Your team? Do you run your own mail server? Did you code our own OS?
This is rethorical of course, all the answers are no.
What exactly is wrong about trusting one more layer to 'experts'?
Not all dev teams can afford a backend ninja just as they cannot afford a network admin or a telecom engineer. Companies like Parse are on the right track, they provide a much needed service.
I've been on this trade long enough to witness the transition of companies hosting webservers in-house to realizing a dedicated server made more sense (one team of experts managing many machines), then VPS, then containers....then BAAS.