Neither the Florida or US Supreme Courts declared a winner. They simply ruled that the recount should continue/be stopped.

There is nothing in the US constitution that would allow the US Supreme Court a winner. That is the job of the House of Representatives. Gore didn't want the House of Representatives to do that, because he would have lost. Hence, Gore & the Democrats decision to use the courts instead of allowing a tie to be declared, and the tie breaking vote to be taken by the House of Representatives.

The Constitution is ambiguous on these matters, which defacto allows the unelected, non-appointed power brokers to fight out the electoral battle. We the people don't have any say in it. That much should be obvious after the 2000 debacle.