During the transmission, the generated electric power is delivered after stepping up to hundreds of thousands or even more voltages by transformers.

In that case since \$P=I\cdot V\$, increasing \$V\$ reduces \$I\$ in the secondary of the transformer.

The reason given is to reduce \$P_{\text{loss}}=I^2R\$ losses. Here \$I\$ decreases so the power loss.

Is that the real reason to step up?

I'm asking because we can write the power loss equation as:

\$P_{\text{loss}}=\frac{V^2}{R}\$

Or if we use both \$I\$ and \$V\$ in the power equation:

\$P_{\text{loss}}=I\cdot V\$

It seems like if we step up the voltage \$I\$ decreases but \$V\$ increases. How about the power loss?

Does the power loss decrease? Or the real reason to step-up the voltage is to reduce the cross section area of the transmission lines significantly?