You pretty much will always need a bundler, unless you write everything from scratch, and don't support legacy browsers. Webpack actually does do things like code splitting for you, so no, not everything goes into one file.
What is the benefit gained from "code splitting"? Would it make a blog run faster? What if the largest amount of JS on your site is 5k? Why would there be a need to code split this?
Code splitting is great on bigger webapps such as GMail or Facebook. For instance, when you want to see your contacts on gmail, it can load the required JS file of that module on demand. Same thing on FB: the chat widget can be loaded separately, and only if needed.
A while back I went through the process of evaluating a lot of build tools, and I simply couldn't see any benefits of replacing my bash scripts with these tools, and you cleared it up nicely.
Also, yes, HTTP2 throws in additional considerations, though the surprise for me is that I've found even with direct filesystem access like in an Electron app, with no "connection overhead" like HTTP1.1, webpack bundles can be quite effective for performance gains. Especially with modern ES Modules, it can still be extremely effective to load a sequence of larger tree-shaken JS file all at once than a large number of tiny files.