I support it not due to historical accuracy or composer are god mentality or "purist" reason. Simply due I prefer the aesthetics and the sound of period instruments and HIP performance practices. There's a raucous almost rock and roll mentality vibe I get from listening to a well made HIP performance (due to fast tempo, lack of vibrato which usually give the smooth sheen sound from modern orchestra). There's a sense of a bunch of musician getting together and having a good time atmosphere with the HIP performance rather than the monolithic epic nature of modern orchestra (which is actually in line with the spirit of classical and baroque era works)
I couldn't get into Brahms symphonies until I've heard period instrument performance from Gardiner and more subdued modern instrument performances by Szell because I found it overblown done by other conductors.