Four reasons, expounded on in official Rogue One novelization by Alexander Freed, all in Chapter 2.

1. Because he was ordered to by General Draven.

   He thought back to his conversation with General Draven in the hangar. The assurances of trust, of confidence in Cassian’s judgment, were swiftly being pulled into the amorphous eddies of his memory, but Draven’s orders were etched in steel:
   Galen Erso is vital to the Empire’s weapons program. There will be no “extraction.”
   You find him, you kill him. Then and there.

   However, you're right, he wasn't JUST blindly following orders. He fully agreed with them, for three more reasons:

   Draven wasn’t wrong to want Galen Erso dead. It would be a righteous killing as well as a practical one, ...

2. The execution was of someone that Cassian saw as guilty for the deaths of civilians.

   ... the execution of a man surely responsible for the deaths of countless civilians. Erso’s years inside the Imperial war machine could have no innocent outcome.

3. And, had he not been killed, he could have cost more innocent lives by continuing to work for Empire

If killing Erso saved a single life, then that was cause to celebrate—but if not, his assassination was no less justified.

You claim in the question that "Andor has just witnessed the destruction of Jedha City from the Death Star, meaning it was too late for that" - but that's not really a valid assumption. He could have continued to work on Death Star (say, something broke or didn't work right). Or on the next, even worse, project.

4. And, on top of that, killing him would free Mon Mothma from her quixotic idiocy of trying to follow her futile "present him to the Senate" plan

   Nor did the contradiction between Mon Mothma’s orders and those of General Draven trouble Cassian. The notion of bringing Galen Erso to a Senate hearing—of exposing the Empire’s planet killer, of creating such an uproar inside the civilian government that the Senate would move openly against the Galactic Emperor—was absurd on the face of it.
   Mothma desired a leveraged détente—a political solution made possible through rebel military action—that was, to Draven and Cassian, self-evidently impossible. The Imperial military was loyal to its commanders, and its commanders believed that they, rather than the Senate, already effected complete control over the Empire. They were right. No peaceful transfer of power could occur.
   Yet Mothma was an idealist. Cassian suspected she wanted a Senate hearing not because she thought it would work, but because she felt obligated to try. Cassian admired Mothma. Galen Erso’s assassination would free her from the obligation of a doomed peace effort.

Four reasons, expounded on in official Rogue One novelization by Alexander Freed, all in Chapter 2.

1. Because he was ordered to by General Draven.

   He thought back to his conversation with General Draven in the hangar. The assurances of trust, of confidence in Cassian’s judgment, were swiftly being pulled into the amorphous eddies of his memory, but Draven’s orders were etched in steel:
   Galen Erso is vital to the Empire’s weapons program. There will be no “extraction.”
   You find him, you kill him. Then and there.

   However, you're right, he wasn't JUST blindly following orders. He fully agreed with them, for three more reasons:

   Draven wasn’t wrong to want Galen Erso dead. It would be a righteous killing as well as a practical one, ...

2. The execution was of someone that Cassian saw as guilty for the deaths of civilians.

   ... the execution of a man surely responsible for the deaths of countless civilians. Erso’s years inside the Imperial war machine could have no innocent outcome.

3. And, had he not been killed, he could have cost more innocent lives by continuing to work for Empire

If killing Erso saved a single life, then that was cause to celebrate—but if not, his assassination was no less justified.

You claim in the question that "Andor has just witnessed the destruction of Jedha City from the Death Star, meaning it was too late for that" and "someone who no longer posed a threat" - but that's not really a valid assumption. He could have continued to work on Death Star (say, something broke or didn't work right). Or on the next, even worse, project.

4. And, on top of that, killing him would free Mon Mothma from her quixotic idiocy of trying to follow her futile "present him to the Senate" plan

   Nor did the contradiction between Mon Mothma’s orders and those of General Draven trouble Cassian. The notion of bringing Galen Erso to a Senate hearing—of exposing the Empire’s planet killer, of creating such an uproar inside the civilian government that the Senate would move openly against the Galactic Emperor—was absurd on the face of it.
   Mothma desired a leveraged détente—a political solution made possible through rebel military action—that was, to Draven and Cassian, self-evidently impossible. The Imperial military was loyal to its commanders, and its commanders believed that they, rather than the Senate, already effected complete control over the Empire. They were right. No peaceful transfer of power could occur.
   Yet Mothma was an idealist. Cassian suspected she wanted a Senate hearing not because she thought it would work, but because she felt obligated to try. Cassian admired Mothma. Galen Erso’s assassination would free her from the obligation of a doomed peace effort.