Fact remains, without Blairite interventionist doctrine NONE of this would have happened.
Hang on a minute here. Let's not pretend the Iraq invasion was Blair's work alone. GWB, or the people 'advising' him, were itching to have a go at Iraq since 9/11 and probably before that. The UK contributed about 12% of the personnel involved in the invasion and subsequent occupation, all told. Yes, having the UK as a partner was important to the Bush Jnr. administration in terms of giving the appearance of a 'coalition', but it was always going to be an overwhelmingly American venture and would probably have happened sooner or later even if Blair had refused to have anything to do with it, or if MPs had voted against it.
And even in the total absence of an invasion, it's foolish in the extreme to try and predict what sort of state the country or the wider region would be in now. Saddam wasn't going to last forever and fuck knows what would have happened to the place with one of his even more brutal and considerably less intelligent sons in charge. Perhaps eventually an open civil war between Shi'ite insurgents supported by Iran and the Ba'athist state plus Gulf-backed Sunni extremists. Perhaps an all-against-all conflict involving those three sides, without neglecting the independence movement in Iraqi Kurdistan and Turkey's grotty involvement there since forever, the likely persecution of Christians and other religious minorities, the spectre of another Iran-Iraq war, Israel throwing its weight around in 'self-defence'... yes I warned against predictions, so I'm not saying all of these things *would* have happened, but it's likely some of them would have, in some combination or another.
So yes, without the US/UK-led invasion, the terrible things that happened wouldn't have happened, but other things would've happened instead, many of them no doubt also terrible.