NTSC, PAL, SECAM
Source: https://retrocomputing.stackexchange.com/questions/4896/whats-with-the-atari-2600-colors-on-secam
The TIA manages a very large palette on NTSC and PAL systems because it takes advantage of the way that composite colour is encoded: three bits produce luminance, and the colour subcarrier is always exactly the same sinusoid, but four of the other colour bits set its phase.
So for both NTSC and PAL:
three bits set the amplitude of one signal;
four bits set the delay of another signal; and
the two things are summed for output.
To verify this, look at an NTSC colour wheel, and look at which angle each of the Atari's NTSC colours appears. They're just steps around the outside of the colour wheel.
Even PAL suffers a little from the NTSC-first logic; it has 12 hues instead of 15 because the NTSC subcarrier is approximately 12/15ths the frequency of PAL's, and the delay steps are NTSC oriented.
SECAM doesn't work in the same way. Performing a phase shift doesn't actually make any difference — the colour subcarrier is a single channel in frequency modulation, not two channels in quadrature amplitude modulation. Nothing about a SECAM output is determined by phase. The colour-shifts that result from phase errors is exactly what SECAM sought to fix.
So more complicated electronics are required, and the elegant hack of just doing a phase shift isn't available. More logic is required, and Atari did what it was cost effective to do, which is to implement a palette much like the other RGB-oriented machines of the era.
In short: the Atari's disproportionately-good palette on NTSC and PAL systems is because Atari exploited the way QAM composite encodes colour. SECAM does not use QAM. Therefore a much more basic palette, closer to other machines of the era, was implemented.