Emirates have the critical mass to stand alone. So far they have maintained profitability. The other two have opaque finances. Nobody really knows if they make any profit. Continual expansion without profitability will increasingly draw criticism of over capacity, seat dumping, and State subsidy. This will limit their growth and could be their undoing.
Forging alliances is a way to mitigate this and reduce subsidy scrutiny.
Alliances dilute competitiveness. Price fixing, sold to passengers as convenient global connections.
Emirates have avoided global alliances. As long as their finances remain good, this will not change.