But failing to undertake a proper root cause analysis is harmful to your stated aims.
You appear to believe that a resurgent radical Islam is primarily due to the rise of wealthy Arab states, and yet these states are aligned to the West, armed by the West, and also suppress the same radical elements you wish to neutralize domestically.
A proper root cause analysis would reveal that violent military intervention coupled with Western political soundbites (which have a modern crusades theme to them) are the real factors responsible for radicalizing elements of Middle Eastern society.
Western and Middle Eastern political organizations with a religious base, radical pastors and imams, and military contractors seem to be the main beneficiaries in this culture war, and domestic citizens in the Middle East and the West seem to be the main losers.
Civil liberties are eroded domestically, a constant state of fear is generated domestically, and travel options internationally are limited. This applies to both Middle Eastern and Western domestic populations.
The simplest and most effective solution is, you say, to limit immigration and assimilate existing immigrants? Historically maybe it's been the 'simplest' approach, in terms of isolating and subjugating 'foreigners' (apart from slavery), but I wouldn't agree that it's been effective in neutralizing resistance to whatever was the hegemony of the age.
Instead I would look at the success of Western countries in cultivating an apathetic population as the counter-intuitive solution for a continued hegemony. Rising living standards, opportunity, and entertainment as distraction.
Look at how China invests in significant infrastructure in Africa to buy stability and access to natural resources. The idea of foreign aid is certainly not new, and the world is littered with US-funded roads and hospitals, but the ratio of destructive / constructive actions is completely the wrong way around.
Why not wage peace, allocate more of the loot to local populations so they see a significant rise in living standards, and cultivate a widening middle class that has less reasons to be sympathetic to radicals?
That seems to me a far more sophisticated approach to exerting and maintaining influence than the traditional "wage war" approach.
Your position seems to be a result of artful misdirection which paints militant Islam as the cause when in fact it is simply the effect of the militant West. It's the bitterest of ironies that the global Defence industry is in fact one of the greatest enemies of continued goodwill and peace for Western populations.