What bilge...
The SCOUS simply stated that the criteria used by the Florida Supreme Court (which voted 4-3 to adopt a highly selective vote recount) was not sufficient (note that they - the SCOUS - had previously ruled on this very issue, and the Florida SC simply ignored the ruling...), and that the recount could not proceed in its existing form. Given the very short period of time left before the constitutionally-mandated deadline for submitting a vote count would expire, this effectively ended the process. Note that the Florida SC did have several proposed recount strategies in front of it that would have permitted a recount to proceed, but they rejected them in favor of a heavily biased strategy that would have recounted ONLY overwhelmingly Democratic districts, while ignoring all GOP-dominated districts. The Florida SC that did this was highly partisan (in fairness, state SCs typically are), certainly no less (likely much greater) than the SCOUS. The point is that the SOCUS didn't appoint or select anyone, and in fact they had given the Florida SC two separate opportunities to conduct a recount before they obvious bias of that court forced their intervention.
As to what would have happened if the courts hadn't intervened? A second vote was NOT going to happen (this would be unconstitutional on several different grounds), but a disputed ballot might have been challenged in the House of Representatives (the folks who actually vote to certify an election) the week before the inauguration. Given the balance of votes there, it is likely that there would have been any chance in the results, but one never knows...
The partisan nature of the election was (and remains) a point of contention, but might I ask what other outcome would have been possible? Election officials are indeed political (and thus partisan) appointees, a principle enshrined in Florida's constitution. Had Katherine Harris stepped down, who would have replaced her? To listen to some (SOME, not all) of Gore's partisans, only appointing Larry Tribe would have been a satisfactory result, which suggests that the debate wasn't about the process, but more about the outcome. The Florida SC was packed with partisans, and the SCOUS, while somewhat less partisan clearly was split along political lines. Hence this is more a question about which biased court ruling do you want to embrace, not which ruling was unbiased.
A final point, had Bush's brother wished to intervene (and it is important to note that Jeb Bush deliberately and quite publicly recused himself from any intervention in the election mess specifically because of his obvious conflict of interest), it would have been simple enough to have ignore Democratic protests at the beginning, and certified the vote count before the Florida courts could get their hands on the case. Neither Jeb Bush nor Katherine Harris did anything like this, though it would have been simple enough to do.