Why do you think your magic third party will be imune to the same influence?
I agree. We need to abolish all political parties established after Washington. The same should be done for executive orders creating new laws and not affirming existing ones, which are unconstitutional and yet allowed throughout US history.
"However [political parties] may now and then answer popular ends, they are likely in the course of time and things, to become potent engines, by which cunning, ambitious, and unprincipled men will be enabled to subvert the power of the people and to usurp for themselves the reins of government, destroying afterwards the very engines which have lifted them to unjust dominion.” — George Washington
"The alternate domination of one faction over another, sharpened by the spirit of revenge natural to party dissension, which in different ages & countries has perpetrated the most horrid enormities, is itself a frightful despotism. But this leads at length to a more formal and permanent despotism. The disorders & miseries, which result, gradually incline the minds of men to seek security & repose in the absolute power of an Individual: and sooner or later the chief of some prevailing faction more able or more fortunate than his competitors, turns this disposition to the purposes of his own elevation, on the ruins of Public Liberty." — George Washington