As Organic Marble points out, yes the US space program had G meters. They're likely to include these in future manned missions, as well.
As for the true purpose of the toys: To humans, any sudden reduction in acceleration feels like falling. When the engines cut off, they are aware that there is less thrust, but the human body isn't great at telling you, ...
The original shuttle flight deck had a mechanical g-meter on the instrument panel. A reading of near-zero here was a cue that free fall had been achieved.
(NASA photo, emphasis mine)
When the shuttles were modified to the 'glass cockpit' configuration, a virtual g-meter was included.
(reference, p. 2.7-15)