Well the Sportwashing is working for Abu Dhabi and Qatar.
Dubai was a desert years back , now it's a holiday City . Qatar has now good relationships with France Goverment.
Saudi Arabia realised it too and now wants a World Cup and takeover Newcastle. Their emergency Plan is a Serie A club if PL keep on blocking the takeover
Well Dubai modernisation plans started before the Arab football investments. I think it is the Abu Dhabi group behind City and not Dubai though.
They are definitely using the clubs as a vehicle to build business opportunities to the Nth degree.
Peter Lim intention was the same with Valencia, as was Tony Fernandes with QPR and Al Fayed back with Fulham in the early 2000s, but they didn't/don't have the capital to fully exploit it.
For the Arabs it is about building sustainability for long term income post oil reserves.
The Saudi getting into football is similar, with their new crown prince being closer to the US, moving away from Islam and opening the country to new streams with events like Boxing, WWE and perhaps a football club as a vehicle for European partnerships.