You can have brushless DC as well, but its all a balancing game of cost over its lifetime.
Efficiency only matters when the entirety of the process is considered. One high efficiency process can be useless if it forces you into a low efficiency one later.
AC can be generated directly off something that rotates. If you smooth it out to DC, you lose some energy from that conversion.
AC however incurs loss in transmission due to capacitance in the lines so it is more efficient to transport High Voltage DC. Both AC and DC drop in voltage when current flows through anything so you need sufficiently high voltages to do anything at the endpoint. AC is easy to efficiently convert to other voltages - higher or lower. DC can only really be reduced somewhat efficiently. Increasing DC voltage usually involves some intermediary AC step.
If you need AC at the endpoint - motors and compressors as opposed to battery charging, you incur losses to convert it from DC - this applies to DC motors as well which make that conversion internally.
If you are generating AC, transmitting over something with low enough capacitance (turns into a balancing game of resistance, capacitance and space) and can use power at the same frequency as the source, a nicely phase aligned setup can get you more efficiency with AC. If your use is very close to the source though, you might be better off going mechanical though.
Now a lot favors DC - powering semiconductors, charging batteries, and variable frequency compressor tech is mature (that's where you generate a custom AC signal based on the need rather than turn on and shut off a fixed frequency AC compressor based on need). AC still wins at turning a fan or continuously running compressor or something of that sort, and most importantly - changing voltage to what you need.