Triac control circuit through load
Why is it that in every triac analog dimming circuit I find that the triac triggering circuit is fed through the load and not straight from the mains?

In most countries there is no neutral available in the wall switchbox where the dimmer is mounted. Arranging the circuit to find a neutral path through the load avoids having to rewire the switchboxes with neutral so it is a rather clever trick.

Figure 1. A typical incandescent dimmer circuit with no direct neutral connection. C1 would typically have to charge to about 20 V before DIAC1 conducts. Source: LEDnique -Triac.
The downside is that the triac can never be on for the complete 180° half-cycle as the voltage may need to increase to about 20 V or so in order to trigger the triac through a diac - the normal control circuit.

Figure 2. The upper trace shows the trigger delayed close to the end of the cycle. The resultant effective voltage is low. The lower trace shows the trigger close to the start of the cycle. This will result in close to full voltage but note that this can never be a full 180°. The relationship between phase angle delay and resultant RMS voltage is graphed on the right.
For a little more reading see my linked article.