I respect that there are vulnerable players out there. However, there comes a time when those players need to see that the internet has scary things on it. Trying to hide that ... it's only going to lead to a worse situation later on. At least this is only a game; what happens when they move into more "important" (loosely used) things? I'd rather they experience these facets of the internet here, where there's little potential for harm, rather than the "real world" side of the internet.
I'll include this tid bit here, quoted directly from the RuneScape Terms & Conditions.
6. Safety and abuse
Before using any Jagex Product you should read Heath and Safety information and Safety and Security information. Parents of those under 18 should also review this information.
We are under no obligation to (and do not) monitor User Content. You should be aware of the potential risks of using a service which includes extensive User Content. User Content may be inaccurate, out of date or otherwise inappropriate. We cannot guarantee that users will comply with our terms and conditions, rules or otherwise behave appropriately. You should not assume that a person is who he or she claims to be. In your own interests, you should not attempt to contact any other user outside a Jagex Product.
If you are the victim of offensive or inappropriate behaviour or receive any other unwanted communications, you should use the built-in blocking facilities (as detailed in the Chatting and staying safe online section) to block the messages. You should report all inappropriate behaviour to us via the in game "Report abuse" button as well as seeking appropriate external help, for example from parents or law enforcement authorities. If you continue to suffer problems, or are not satisfied, then you must stop using the relevant Jagex Product(s).
Jagex knows their PMods aren't a suitable guarantee of a safe gaming experience; that's why you agree when playing to use their built in functions (ignore list, report abuse) when faced with a dangerous or potentially harmful situation.
Also, I'll just add that I used to be a kicking rank within one of the penguin FCs that you mentioned. At no time were we crippled due to a lack of in-game muting abilities among the chat. We took full responsibility of protecting the chat, often communicating between ourselves as ranks to make sure there was someone (if only idling) in the chat at all times. In my opinion, it is the group coordinating the service, who holds the responsibility of keeping that chat safe. If they don't, everyone is free to find another service. There is no applicable need for PMods to use that service for the purpose of serving as a moderator. If anything, their ability would usurp those serving as leaders in the chat, oftentimes causing more confusion. (I was accidentally muted by a PMod while kicking mass-spammers from a penguin chat. But that's a story for a different day. )
All in all, we players have the ability to protect ourselves from harmful content, and we are expected to do so (as per reading the T&Cs). There is no need for PMods, they are merely a sour convenience.