In my opinion what has exploded the complexity is the proliferation of environments. The execution environment of our software provides very few guarantees on what is available (no standard library) or even what language is supported (many JavaScript features and versions with varying support). That, combined with the explosion of devices including input modes, screen sizes, and resolutions has just made it extraordinarily difficult.
We don't even have standard ui primitives like we did in the past. Every major website is expected to have a team of world class designers and reinvent the wheel.
It doesn't need to be this way. But it's the way we have chosen. It has advantages, but I'd imagine the economic cost is enormous.