I feel like in reality that other kingdom's prince is bound to backfire for a lot of reasons, assassin might mingle among the ladies, no crowd control, there should also be an eccentric person who would cause a scene who refuse to leave after shaking hands/hug, etc.
Even without any mishaps/accidents on his side he's bound to lose.
Both side are misunderstanding that they need to make more money to win, but that's not really the case.
The competition's 'goal' as suggested was for prosperity of the town, with criteria of who's more popular.
https://mangadex.org/chapter/678e7e15-26c9-4bf6-bf96-28cd51ef6233/9
In term of value for the town, the prince offer nothing.
His goods are from the empire, he's only staying here temporarily.
Once he's gone, the town will go back to where it was.
His target is primarily women only.
Meanwhile Elizabeth specifically incorporate the local hot spring into her stores and have various services to cover for all type of folks.
So even though this chapter is foreshadowing his business plummeting (and for some ego crushing) soon by the way that aide just casually push aside a girl and essentially tell her to 'give us money and fuck off', I think by the end of things he'll still lose even without that.