I use the term web script to define any pre-made code you use on your website. cPanel provides installers for those scripts but does not automatically update them. It is a good security practice to either password protect, or remove anything that you don't use when it comes to pre-made code. If you don't keep up with updated releases then it will eventually fall out of date and have the potential for an exploit to exist in the code.
Your correct, those are a bit dated but are the correct procedures, here is a link direct to cPanel's documentation.
However, if you want you can simply open a support ticket with us and let us know what you would like upgraded.
Generally speaking MySQL and Apache don't have to be updated very often.
Apache its self has very few if any compatibility issues when going from version to version, so it is safe to keep this at the latest version of your branch. (2.2.X or 2.4.X)
MySQL is very much the same way. In regards to common scripts MySQL has not made many changes that would cause problems, there are a few things that changed between 5.1 and 5.5 (5.5 being the latest) but primarily you won't have to worry about upgrading MySQL near as often.
PHP is what generally gets developed on and upgraded the most. The problem with PHP is they constantly add and remove what they consider to be "valid" working code. So a php script written for php 5.1.X may not work in php 5.4.X. If your upgrading from say 5.4.6 to 5.4.21 then you'd be safe, as code is not changed in minor releases. Generally these are security patches and bug fixes. It is only when you go from major releases (i.e. 5.1 to 5.4) where you may see compatibility issues. Good news is, if an upgrade causes issues you can generally downgrade until you isolate them.
I would agree to an extent about your analogy with computer updates. Wait a little bit, ensure they are stable and then apply them. The only other step would be to look @ any software your using to ensure that it is also compatible with it, primarily in regards to PHP.