I think the problem is when matters get referred to the court to...

I think the problem is when matters get referred to the court to decide on sticking points in the process. For example under "Article 23: Terms of Reference":
2)
The Terms of Reference shall be signed by the parties and the arbitral tribunal. Within 30 days of the date on which the file has been transmitted to it, the arbitral tribunal shall transmit to the Court the Terms of Reference signed by it and by the parties. The Court may extend this time limit pursuant to a reasoned request from the arbitral tribunal or on its own initiative if it decides it is necessary to do so.
3)
If any of the parties refuses to take part in the drawing up of the Terms of Reference or to sign the same, they shall be submitted to the Court for approval. When the Terms of Reference have been signed in accordance with Article 23(2) or approved by the Court, the arbitration shall proceed.

If we are under the older rules that 30 day time limit is actually 3 months.
There are also earlier possible sticking points in the selection of arbitrators. Such as under Article 12: Constitution of the Arbitral Tribunal and Article 14: Challenge of Arbitrators.