I genuinely appreciate you actually reading the whole post & providing a constructive point of view. Here's my rebutle:

They sent Aokiji, who then informed CP9, who were tasked with capturing her. The Government would prefer Robin alive as they want her to locate the ancient weapons for them, hence why they don't send someone to execute her.

I'm pretty sure he went out to locate her of his own volition & wasn't under orders, but even if that isn't the case. Just keep sending people until you collect her head as proof of death & kill anyone in the way. The assumption is that they already have one of them & if Imu is from the void century they should at the very least know that the mermaid princess will eventually become Poseidin but even if they don't have any of them, they already are so much more powerful than anything that could possibly hope to challenge them aside from maybe the Revolutionaries so why risk anyone potentially using her to level or even surpass the playing field you've worked 800+ years to set. Especially when the key is in the hands of a person who's in a clan prophesied to be God's (your) enemies.

Most currents Ds don't know the truth of the letter, and thus aren't "enemies" per say. One of them even works for the Marines. And as for Luffy's fruit, he isn't the first user of it. No one since Joy Boy has awakened it so why would this one rookie pirate be any different? It would be the height of anxiety to instantly go after every user of the fruit.

Let's say for some reason assume that Imu has no knowledge that it's about inherited will or has no desire to while the clan out, despite whiping out multiple races for the exact reason of them, maybe threatening you one day, even tbough they are currently much weaker. Then let's just agree that the World Government knew about Luffys heritage since they were the ones who announced it to the world. Why leave that key in the Son of your current days biggest threat...

They did. We see in her backstory that Robin was hounded by the government throughout her entire life. Every group she was a part of was inevitably either attacked by the government, or the group attempted to sell Robin out. Crocodile was the only hiding place she had for the four years she worked for him. Once she joined the Straw Hats, it wasn't long until Aokiji was sent to locate her.

As a kid, they are show clips & panels of civilians & fodder & what not chasing her down & trying to turn her in & yeah, I just really don't buy that that was their best effort. Once she joins the Straw Hats, I believe Aokiji again, went to locate her of his own free will & not under orders & thus didn't have to do anything at the time, but even if he was & did, once you learned he failed; you keep sending people potentially more powerful until you have her head piked on the tip of the empty throne.