I agree, the people do not directly elect a "national leader". But their peers choose the one that then the public will choose or not choose. So in the end they are, if not directly, electing a national leader. If the party doesn't put forth a candidate that people will vote for, thats their fault
But the leader who ran and lost, can either resign, or decide to carry on as opposition leader. Or a third option that the party holds a leadership review and maybe forces a new party election.
But when the dust settles......there is one and only one top voice that defines that party in opposition. Here in Canada, Pierre Poilievre, who caters to the maple maga, lost the election, but still speaks as the most authoritative voice for the official opposition. Even immediately after the election.
In the US, it is even simpler, because you only have two serious parties running. So it just seems odd that the person, Kamala Harris, who had almost half the votes and support, had great momentum to build from, with overflowing arenas, did not stay in the spotlight, and be regarded as the voice of Democrats. Until any new primary was called for by the party.
To just cut off all momentum like that just seemed counter productive