When the actual logic resides deep in a call stack, it's more difficult to debug code, much less bring on new developers. Each additional abstraction layer is, unsurprisingly, another layer that you're going to have to trace through to get at the root of the issue.

Similarly, when your logic doesn't reside at the root level, it's easy to accidentally bypass. Perhaps this is intentional, but I'd argue that intentionally bypassing certain logic under certain conditions indicates your logic is poorly factored. My most common example to this is an admin panel: admins can, as an example, change any user's name, not just their own. However, this only holds true when in the admin panel. So in your user controller, you have some sort of permission check ensuring that the user being operated on is the one authenticated[1], but intentionally don't place that check in your admin controller. One day in the name of a better UX you add an AJAX component to this, and forget to copy across that check into the ajax endpoint. Suddenly I can change anyone's username, despite not being an admin.

To solve this, we've created a couple of libraries: PermissionCheck and AuthContext; the former (typically) depends on the latter. AuthContext answers the questions of who are you (authentication) and where are you (context), and the permission check wraps up the authorization component: in the (web frontend | api | admin panel | cronjob | upgrade script) does the currently authenticated user have permission to do X on object Y? By putting these checks in the models, it's easy to ensure they're always enforced (a user's updateName method may call checkUpdateName()->enforce() ); if you want to side-step (or ramp up) authorization under a certain context, you edit the model's permission check for that action, rather than one or more controllers.

Could you put that into a different helper library? Probably, if you were so inclined. However, that leaves you with at least two files to check when you want to examine behavior, and an inability to use any protected or private methods from these permission checks.

Having an object that does a lot of stuff is not necessarily the much-feared "God object", although it certainly can become that. I've learned to become more fearful of the "God methods" instead; having 300 10-line methods doesn't concern me nearly as much as 10 300-line methods. Breaking code apart simply because you want a smaller file means you have a crappy text editor. Break code apart when it's logically doing more than it should be doing, or is poorly encapsulated.

This is, to a limited degree, an issue I have with mocking in unit tests: while great in theory (test components individually and trust that your interfaces/contracts/whatever ensure that A and B independently working mean that in production they will work together), in practice the two components do have a dependency on each other, and it's exceedingly difficult to reproduce production issues because of that fake isolation. How many ways have you seen an external API fail? Have you reproduced those failure modes in your mock, and have you written tests against each one of those different modes? Maybe it's the industry I'm in (payments), but in a world made of edge cases, effectively squaring the number of scenarios I have to test is not a pleasant experience.

/edit - forgot my footnote :)
[1] In practice, a user controller will hopefully tend to always operate on the currently-authenticated user, rather than passing around a userId by whatever means. However I've seen the latter done, and this exact kind of problem is what ensued.