There are a few reasons it is better to send electricity with high voltage instead of high current.
1. When voltage is increased, the current is decreased. Along any transmission line, there is electrical resistance, and those losses are increased much more with increased current. So lower current means less energy lost due to resistance.
2. Lower current in a line means that the line itself (the conductor) can be smaller. A smaller (thinner) transmission line is easier and cheaper to produce.
3. Because the transmission line is smaller, that means it is lighter. Lighter transmission lines means that the support towers holding them up do not have to be as robust. They can be made of cheaper and lighter-weight materials.
All of the above result in significant net savings for the power companies that are producing and transmitting the electrical energy. That in turn, hopefully, reduces the costs being passed on to the consumer.