The third party rules, like many other amateur radio rules, are there to protect amateur radio spectrum from commercial users. The "non pecuniary interest" clause is repeated in several such rules, not just the third party rules.
The thought here is that amateur radio gets use of the spectrum for free. If it allowed for someone with an amateur radio license to be paid to transmit, then commercial interests could leverage this to get "free" access to the spectrum, crowding us out of our spectrum (perhaps broadcasting music and advertisements) while simultaneously competing with other services (like the phone company and commercial radio stations).
The third party rules are there to allow us to pass message traffic and do things like allow unlicensed operators to talk on the radio while the radio is controlled by a licensed operator, which is great for introducing amateur radio to new people. The restriction on third party rules is in part to prevent commercial abuse and other abuses.
This might seem silly today, but there is historical precedent for these issues actually being a problem, and date back to 1910 when the regulatory structure for radio spectrum was originally created. I don't think the need for this regulation is different now than it was then. (While not directly relevant to this question, prevalence of pirate radio today is evidence for this.)