I think it worked. I dunno, I think it's something that even foreigners can evalulate for themselves: in the context of racial tensions in the 60s, ideological warfare against communism, and an overall spirit of "American bravado", does a pledge make sense? As a ritual, it will have a unifying effect, even if we were reciting proper tooth-brushing etiquette at the beginning of every game. The effect would reinforce awareness of the pledge and what it stands for. Also I think a direct comparison between UK and USA is insufficient. this is more like UK versus other European countries in a football game. Are flags not waved and anthems played there?
The idea of saying your pledge or standing behind the anthem as ideological warfare against your rivals in sport is nothing new either. Way back at sacred games in Greece, the hellenes would pledge loyalty to a given city and/or diety and would give speeches (sermons, essentially) to that effect. The winner of a game could bestow the trophy/prize to a temple as a show of honor/humility, increasing that temple's notoriety. They would also compete on behalf of patrons, who wanted the political clout that went along with sponsoring a winner at the games. There were competitive categories in singing and music-playing at the games, too (which isn't a sport but gives a glimpse into their culture/mindset).
Fast forward to today and saying a pledge that reminds the participants that we are Americans doesn't seem so bizarre. Some families even say a prayer at Easter dinner.