Okay, so first of all, what use is either type of ‘ball’, e.g. ‘football’ or ‘testicle’, when pursuing a claim or needing legal representation? Would a judge be swayed by a quick kickabout or display of balls? You’d hope not. And while the first scenario might be fun to imagine, genitalia, for so many reasons, have no place in a court of law.
But then the wordplay is of course all about communicating the attributes associated with ‘balls’. ‘To have balls’ is linked to ‘courage’, so ‘representation with balls’ is meant to have positive connotations. However, ‘having balls’ is not always a good thing. ‘To have someone by the balls’, for example, means to ‘[h]ave complete control over someone or something’ (OD). And a ‘balls-up’ is ‘[a] bungled or badly carried out task or action; a mess’ (OD).
So maybe this whole balls-business is not such a good thing to evoke after all? And if it has to be a reference to reproductive organs, why not pick ovaries instead? Unlike balls, they can’t be kicked.