Being wary of large corporate engines is a good piece of advice. "Make a game engine from scratch" is a terrible recommendation and shouldn't be linked to the first one. Every dollar and hour spent on a custom engine isn't being spent on the end result. There's a place for it, sure, for people like Blow who are in love with the craft--but most indie game devs don't want to make an engine, they want to make a game.

Maybe, maybe not. Watch this talk https://www.youtube.com/watch?v=RsT-5VSqk8I

There are also costs to use the ecosystem of an engine, as you need training and experience. The main advantage is that an ecosystem exists that can provide advanced tooling and resource management. There are quite a few alternatives if it is just rendering and general media playback. There are some generic frameworks to develop games, but most rely on custom architectures. Adapting the read-to-use engine takes time as well.