PHP Notices – How Important Are They?

I code to E_STRICT and nothing else.

Using empty and isset checks does not make your code ugly, it makes your code more verbose. In my mind what is the absolute worst thing that can happen from using them? I type a few more characters.

Verses the consequences of not using them, at the very least warnings.

The purpose of modules and frameworks is not so much to achieve independence of functions as it is to achieve reusability and flexibility. In most other occupations, this kind of reuse of function and flexibility is central to achieving success.

Think about how difficult it would be to work on your car if you had to buy a whole new tool set for each car, because the tools were not interchangeable. Or worse, you hae to build the tools from scratch, because there wasn't a factory to create them. Both of these concepts (universal pluggability and object factories) are present in well-written modules and frameworks.

...but each project is different and usually involves building many layers of abstractions to add new features - or editing the files directly to customize them. I can't re-use the same module on multiple projects.

You are describing tight coupling, an undesirable trait of software that's intended to be reused. Properly written libraries, frameworks and modules achieve loose coupling through software patterns such as Inversion of Control, message passing, and universally-understood communication methods such as REST and XML. These are not the only methods by which loose coupling can be achieved.

Obviously, it is impossible to write a completely decoupled system; one part of the system has to know something about the other part of the system, or nothing gets accomplished. But a high degree of decoupling can be achieved nevertheless.

Writing modular software takes more work and forethought than writing tightly-coupled systems, but the effort can be worth it, especially when writing a framework or library that will be used by many people.