The way I see it, a master is more responsible to the community than to the event organizers. If he fails at his task he should suffer more consequences from the community (losing respect and people's support in the next trials). To be exact, IMHO it's fine if his penalties for failing in a PvP event are the same as any other person's. (By the way, he already suffers enough emotionally from the fact that he failed to promote the element he loves.)
And a master's responsibility is to promote his element by any means he sees fitting. If he is good at PvP then he will probably do so by leading a war team and taking part in other PvP events as well. Although, if he is better at PvP than he is at leading and organizational skills then I think he should be allowed to put all these responsibilities on his Lieutenant's shoulders, effectively making him the real general.
On the other hand I can perfectly imagine a master who is an average PvPer at most, but makes up for that with other activities like being a card curator, council member, or even just a creative person who promotes his element with artistic skills. I think it's perfectly fine if such a master doesn't even participate in the war, although he will probably feel some pressure from the community to join, so this probably would only happen if he feels that other people will really make a better war team, so his responsibility to decide what is best for his element tells him that it is best not to participate.
Anyway, this category of masters probably won't be seen too often, since the rules of Trials require PvP skills (or huge luck) to win. I'm not really sure if it's better that way or not, since some people see masters as purely PvP players, but I honestly feel that representing their element in other fields is equally important, and being the best PvP player of the element in question is not necessary.