Actually, if you want to integrate any other web app, then since Moodle 2.2, then potentially you can, using the External tool plugin, which implements the LTI standard. And then you don't have to use the standard Moodle tools, if you prefer the external tool you have found.
The main arguments for maintaining our own tools, inside Moodle, are:
- The requirements for a tool used in an educational setting, where there are separate roles teacher and student, and teachers may wish to grade or monitor students, are somewhat different to the requirements on a generic tool on the internet.
- We have a set of tools in Moodle that are the results of 10 years of community discussion and development to work out what the requirements for a forum / wiki / quiz system that is used for teaching and learning. It would be silly to throw that away now.
- A suite of tools on the internet will have less consistent UI that a suite of tools build into Moodle, therefore requiring teachers and student to spend more time learning the technology, rather than the subject. (Although that technology learning might be more transferable than learning to use Moodle.)