Don't disagree on the history Gibbon but those of us who don't live for centuries can't afford to take such a long term view. Leading by example is fine but we also have to stand up for own views where necessary. We also need to be alive to future threats.
I would also point out that the fact that Christianity has improved is not any sort of proof that Islam will. A sample of two, one does x, so the other will. Not very sound stats, I'm afraid. Currently Islam is becoming more extreme worldwide not less. A major reason Christianity became more moderate was rising living standards in Christian countries, when people have a decent real life they are less likely to depend on fantasies. In an overcrowded world we cannot be sure that will happen again.
Christianity also had the big advantage that the peaceful message of its main text, Christ's teachings, were at odds with the barbaric practices of the Church and this made it easier for reformers to challenge them. On the other hand the Prophet's words and actions were in line with the very worst of Islam as practiced in Iran. There are many moderate Muslims who are trying to reform the religion and want some passages removed from the Haddiths but they face an uphill struggle against an accepted text.
Do we really want to gamble our future on them succeeding while letting Islam, as it is now, grow in influence in the West?