Appeals of procedural matters also should be allowed, naturally. And procedural errors in ascertaining the facts of the case should cause de novo arbitration (or removal from arbitration and into a jury trial, if the arbitrators insist on making the sort of procedural errors that call their fact finding into question). Otherwise, fact-finding by arbitrators should not be subject to appeal, as allowing them to so be would greatly diminish the utility of arbitration.
Another thing to appeal would be the method of selection of arbitrators, the validity of their credentials, etc. But there should be fairly high bars to these (not sure how to construct them).
Granted, the appeals are unlikely to succeed, but perhaps that is because arbitration typically has an approximately fair outcome? Appeals of typical court cases aren't likely to succeed either, but we don't say that court is therefore unfair.
They do not.
What needs to be avoided is
* people being pressured into arbitration in return for something (e.g. Accept arbitration or don't get a job) * people opting into/out of arbitration based on rulings. So, no deciding to move to arbitration because you don't like a judge, nor deciding to go for a trial if arbitration isn't going your way.