Resistive power dissipation is given by P = R * I^2 where R is resistance and I is current.

A transistor in an "off" state has a very high resistance but no current flow, so power dissipation is very low to zero.

A transistor in an "on" state--that is, fully on, has a lot of current flowing through it but very little resistance, so power dissipation is low.

A transistor in an intermediate state--the kind of state you'd use for modulating an analog signal--has significant resistance and significant current flow at the same time. That means they dissipate a significant amount of power, and they get hot.

For some things, like audio amplifiers, there's simply no way around this and you have to deal with it by using beefier transistors and providing cooling.

For a lot of applications, including stove burners, it's simpler and cheaper to use pulse width modulation or "bang-bang" controls.

(It could be argued that bang-bang control is just pulse width modulation with a really slow pulse frequency.)

Anyway, in engineering you'll see a lot of things where you wonder, "why don't they do X instead, it seems like it would be better?" In most cases (not all) the answer is that yes, it would be better to do X, but it would also be more expensive, and it wouldn't be enough better to justify the additional cost.