When the temple was destroyed about 70 CE, the Aaronaic priesthood was destroyed with it. Judaism, however, entered into the Tannaitic ( Rabbinic) era in which it continues -- thank you very much -- without clergy.  
The evil priest-pedophile scandal -- with its perpetrators and their enablers and protectors -- has effectively destroyed the credibility and moral authority of the catholic clergy. 
The hierarchy has no desire for reform -- look at their actions. As time goes by they will become regarded as nuisances
The slow implosion continues.
While it will not happen in our lifetimes, eventually -- if it is to continue -- there will be a new iteration of catholic christianity without clergy.