I think I recall that the 57-mm Bofors was considered but rejected because its shell was considered inadequate for surface-to-surface fire.
The only mention I can find of the USN evaluating the Bofors 57mm (before LCS) is a note in Friedman's
World Naval Weapons that the USN Foreign Ordnance Review Team considered it heavy compared to the OTO-Melara 76mm and 35mm twin. The inclusion of the 35mm suggests this was in the context of the FFG-7 and PHM armament evaluations, since that was the last time the US seriously looked at the twin 35mm.
This is an odd conclusion, IMO: the Bofors 57mm Mk2 weights ~6.5 tons without ammo, compared to ~7.4 tons for the OTO-Melara 76mm Compact (also without ammo). So yes, in theory it's a bit heavy compared to its caliber, but not once you consider the higher RoF and throw weight of the 57mm. Operationally, they're both very similar. This feels like a reverse justification for a decision already made.
The fact that Italy was a NATO member and partner on PHM was also certainly a factor.
Could the decision to go with the 76/62 on Perry class frigates, partially been inspired by US interest in Italy's Sparviero (sp?) attack hydrofoils
Revisiting this, Freidman confirms that the PHMs nearly got the 35mm as well. I presume that the USN had decided that the two designs would have the same gun, whichever one was adopted. And when the time came to make the final decision, there were concerns about the 35mm (limited burst capacity, inadequate ASuW capacity, reliability issues) so the 76mm won more or less by default.