"why a complainant cannot withdraw an arbitration, which is a private agreement to decide a dispute"
Prior to an arbitration, parties can set whatever ground rules they would like. Binding, non-binding, pistols at dawn, whatever...
<brief digression>
It is helpful, though, to avoid the word "arbitration" in connection with the UDRP. It is very hard to have the results of an arbitration proceeding reviewed in a US court. However, every court which has considered the issue has determined that the UDRP does not measure up to the standard of an "arbitration" within the meaning of the Federal Arbitration Act:
http://ipcenter.bna.com/pic2/ip.nsf/id/BNAP-5KA85L?OpenDocument
</brief digression>
In any event, the UDRP by its own terms, which the parties have theoretically agreed to, has a rule that requires the decision to be posted after it is made. So, yes, if the parties were making their own rules from scratch - they could make the rules say whatever they want.
A weird thing about the UDRP is that it is a dispute resolution proceeding between party A and party B, which results in an order for party C to do something. A UDRP order doesn't require the complainant or the respondent to do anything. The order goes to the registrar. So, once the panel has made the decision, the parties are essentially out of the loop. The registrar follows a simple decision tree - was a transfer ordered? If yes, then wait ten days to see if I have received a court complaint. At that point, the registrar (who is bound by the accreditation agreement to follow the UDRP) isn't taking its marching orders from the parties.
As far as neutrality goes, it is one of the great mysteries how one becomes a UDRP panelist, since there are no posted objective criteria. Prior to each proceeding, the panelist signs a sworn statement of impartiality. None of the dispute resolution providers will challenge that statement, since it puts them into the position of calling one of their own panelists a liar. However, it is not automatically a conflict of interest in a particular case if one of the parties' lawyers was a panelist in some other case involving different parties entirely. My law firm, for example, was founded by a former commissioner of the USPTO. I don't think that gives us any particular advantage, though.
Yes, there are lots of cases where a UDRP panelist represents one of the parties. That doesn't mean they win, though:
http://www.arb-forum.com/domains/decisions/97076.htm
In another case, one of the panelists had previously represented a German bank which had a relationship with the complainant, a German broadcaster. That didn't prevent the panel from finding reverse domain name hi-jacking on the part of the complainant:
http://www.dw.com/press011801.htm