^I dunno why i keep getting drawn into such conjectural useless argument but , anyhow... Was the best of humans Prophet Mohammad pbuh had a lineage of "infallibles", was he offspring of Imam, or his father was offspring of an Imam? So this "philosophy" of pure lineage that has desecnded upon you is really flawed, and by the way i don't think any Mahdi is coming.
He (The Last Prophet) was the offspring of an Imam, The Prophet Abraham to be precise whom The Qur'an testifies for. (Surely, We have made you an Imam of men). If you don't think the sacrifice of Imam Hussain was a pure sacrifice in the Quranic sense, then you can do away with the obvious parallel between 'the ransomed sacrifice' that the Quran talks about in regard To Ibrahim and Ismaeel.
Your whole hajj is based around the movements and events in the Life of Abraham, the Prophet of God, and The analogy to that in the Modern Prophetic sense is to Mohammed and his family, IF you care to take note of the 'Durood Shareef' within your own Salaat.
So, if you fail to ponder upon the obvious reality then your own concept of purity in the form of 'Islamic Personalities' are concerned is also 'flawed' and you have not fully grasped or put into perspective the time honoured teachings as per narrations from The Qur'an in relation to 'family' and 'prophet'.