Leia tried to argue for leniency in the sentencing of captured First Order officers and soldiers. They were brainwashed from youth, groomed just like her son from an even younger age. They were soldiers before they were even grown.

"Yesterday they were child-soldiers, but today they are rabid dogs, extremists, murderers, adults too far gone to recondition and reintegrate. You spare them, they would go right back to being enemies of the Republic, peace, democracy, and freedom itself."

Public executions were good for morale and good for votes, in these turbulent times. The people called for blood, and the senate served the people.

Bonus:
Kylo Ren was given partial custody of Brendol Hux III, Force sensitive, the great-grandson of Sheev Palpatine.

"Lord Ren. If you see this message today, I am likely either captured or dead. I had hoped to ask you of this favour in person, but such are life's failures and surprises. We've had our differences, but I do hope sincerely that in the interest of this New Empire that we all hope to build, in the interest of stability and peace, of our future, that you take this child as your apprentice, and teach him in your ways, as my father and I had taught him in ours." - Brendol Hux II