That is not exact. There is no true concept of first and second field. The two fields don't necessarily are part of the same image.
While the reality may be that each field is different, the NTSC spec clearly defines a frame as consisting of odd and even fields. You have to remember that the spec dates back to the 1930s, with color added in the 50s. A proper interlaced NTSC picture will conform to the spec. The A8 signal is not a proper NTSC signal- it takes advantage of the way the spec was implemented to work.
You need odd and even fields to properly deinterlace a NTSC picture, period. If you don't know which frame you are on, you have to guess which ones to combine. It's what we are stuck with for the next few years, and, yes, it is exactly why your capture cards don't like A8 stuff. The cards expect a NTSC signal and they are not getting it.
As to newer consoles providing a proper interlaced picture- yes, they do and no they don't flicker. They render to a back buffer and copy the buffer to the display buffer in sync to the television signal. You really couldn't do that on an A8 in 1977- memory was too expensive, and you had a 1.79 Mhz processor! (For reference, the NTSC pixel clock is about 15 MHz)
Stupid trivia... the PC 18.2 Hz clock tick and the 1st PC's clock speed (4.77 MHz) are derived from the NTSC colorburst clock)