Electrical – Leakage current in in-line mains filters

Yes, transformers could be lighter. 400 Hz power is used on aircraft for this reason.

The generator wouldn't need to spin faster if it is designed with more poles. Motors would also have to be redesigned to run at normal speeds with 1000 Hz power.

But how often are 60 Hz transformers used in modern electronics? There is a big one on the pole outside of my house, and in my boat-anchor hi-fi amps and tube guitar amps. All the other power supplies in my house use switching supplies that run their transformers at a much higher frequency.

edit: Another thing, transformers tend to vibrate slightly during operation. A 60 Hz transformer will "hum" a little bit. But imagine all the appliances in your house buzzing at 1 kHz. 1000 Hz is two octaves above middle C, and our ears are 30dB more sensitive to this frequency than 60 Hz:

Image source: http://en.wikipedia.org/wiki/Equal-loudness_contour

Use a high power resistor. For any given temperature, resistors will be more reliable than semiconductors, so there is no advantage in dissipating that power in a transistor.

This is common in power circuit design, for example dimmers and switched mode power supplies, you will need high power rated components because you are working at high voltages so even moderate currents produce high power dissipation.

I assume you are using a hard-fired technique, where you leave the gate current on continuously. In that case, the only way to reduce dissipation in the triac gate resistor is to use a more sensitive triac. But there is also the soft fired technique, where you only pulse the gate at the zero crossing and the triac stays latched on until the main current falls to zero. This is not suitable for all loads.