The oil might "just" run out, either way it was obvious to everyone that natural resource-based wealth won't last forever, just like in that Sheikh Rashid quote from around 1988:
"My grandfather rode a camel, my father rode a camel, I ride a Mercedes, my son rides a Land Rover, and my grandson is going to ride a Land Rover…but my great-grandson is going to have to ride a camel again"
They would still have trillions invested across EU and US, if their relevance bothers you then you should direct your anger at the leaders and voters who made them as relevant.
These investments can be easily taxed or regulated so they don't generate any real profit once the oil countries are irrelevant.
Those investments are paying for the generous welfare states that keep GCC countries populations pacified. End that and you could end up like Egypt or Syria, a population even more prone to radicalization and even streaming towards Europe in migration waves. That is not in anyone's interest.
The immigrants were let in Europe because politicians wanted to let them in.