If your goal is to release as fast as possible or create as many games (for some definition of game) in your lifetime, then I guess there's a case against building your own engine or - as I would call it - using libraries.
But big engines definitely have distinct "feels" and can't quite hit certain gamefeels.
There's also the long view: What if I spend 5 years making an engine, learning gamedev and computer graphics, and come out highly expert with an engine built to my tastes? At that 5 year mark, suddenly my engine is better for me than the generic ones.
You may say - there's no guarantee! True. But what if I know I'm technically excellent and that I'd be wasted that advantage of mine by _not_ going that route?
What if I really only want to make a handful of games in my lifetime. Maybe I'll release smaller ones along the way as learning exercises, but I'm fine with spending 5-20 years in the dirt growing and come out the other side with something truly special?
Tools affect your art. Especially programming & gamedev which is so psychic. I may not want my mind tainted by engines with product-mindset values I don't agree with.
The reasons go on.