Why do most guitar amps have a preamp and a power amp section?
Why is it difficult to build a guitar amp with a single amplifier
section that goes from the very weak signal from the guitar, to the
very strong signal that drives the speaker?

An audio power amplifier uses negative feedback to obtain pretty constant gain and low distortion. Trying to build tone controls into this amplifier will severely affect the negative feedback process and, it might become positive feedback. Then your power amplifier turns into a power oscillator.
That is a certain reason why you don't incorporate tone controls into the power amplifier section.
An audio power amplifier has to produce large currents in order to drive a loudspeaker and, the wiring to the power amplifier (if mixed with the preamplifier) will create large problems; speaker drive currents can leach into the input circuits and will create unwanted problems turning your &quot;amplifier&quot; into an oscillator (again). Look up star-point wiring for amplifiers to see why.
This is another reason why we keep low power signal amplification away from the power amplifier.
A guitar requires a high input impedance amplifier such as from a JFET circuit. This type of circuit needs to be largely free of power supply variations that are caused by driving high currents into a loudspeaker.
This is another reason why the front-end (or pre-amp) is kept separate from the power amplifier. Usually a secondary power supply stage is used that has much more filtering on the power rails.
It then makes sense to split a guitar amplifier into three stages: -

High impedance front-end amplifier (specific to normal guitars) that outputs a line-input level signal
Tone control section with some amplification (processing regular line input level signals)
Power amplifier (line input level to speaker)

But, it's fairly uncontroversial to join the front-end with the tone control section so it usually boils down to two physical sections.