Why can't analog video be compressed like digital video (example inside)?
The analog TV signal was originally designed to be decoded with the smallest practical number of valves (tubes). Thus about half the signal space (30% of the signal amplitude and almost 30% of the time) is dedicated solely to synchronisation pulses easily detectable by analog valve circuitry, and the picture information is left with only the other half

Any enhancements over this original specification had to be implemented in a compatible way. Thus the colour signal is modulated on a high frequency carrier that does not disrupt the operation of the underlying black and white signal (though a really good B&amp;W set will show it as a fine speckled pattern). 

Later, other information (in the UK, PRESFAX, test signals - pulse and bar, one line of colour bars, CEEFAX/Teletext and closed captioning) were "compatibly" squeezed into nominally invisible "unused" lines during the field sync, but in practice you could see the moving dot pattern at the top of a badly aligned screen.

Compression could not be implemented in such a compatible manner ... how would you store a few lines of picture? Here's a box of tubes, have at it! When colour came along, a single line of low-bandwidth colour signal was stored in a delay line, for either delay-line PAL, or SECAM "Sequential Colour with Memory" decoders, but that wouldn't have been cheap enough before the mid 1960s. I think the delay line was a SAW (Surface Acoustic Wave) device.

In any case, signals as regular as your colour bar test pattern are too rare to be worth optimising. And if you saved some signal space on a simple picture, what would you do with it? A complex signal like a more typical picture needs the full bandwidth anyway.