The phrase "Solomon's complete obliteration" does not mean that all traces of him disappear, but rather that everything that is his to do has been completed and finished.
...All living things, when they meet their ends, have "unfinished business" that they leave behind. This is something true of everyone, regardless of how perfect a life they may have led.
The path of human history is created when the people who follow pick up and bear these "leavings".
And a complete obliteration means to ascend from this path-
to complete everything one has been tasked with, and to reach a state of existence in which there is "nothing left to do".

There is no longer a need to defeat him, or rely on him.
No longer, will anyone ask of him,
or need to shoulder his death,
and no further help or accomplishments from him will be sought.

The means a disappearance from even the Throne of Heroes.
A release from the duties of one's existence, a completion of all the tasks for one to do in this universe.
In contrast to the savior known as the only one among humanity to achieve enlightenment, the coward has reached a different sort of "destination".

Ishtar is still herself despite manifesting as a servant without much difference. The only significant effect Rin has is granting Ishtar perseverance which the goddess never learnt since she was well-protected by her Almighty Father. Ishtar understood and appreciate the importance of hard work and thus altered her thinking despite Rin's personality was never surfaced like Waver's case.

I'm the most beautiful, and I will work hard to improve myself if there is one that is even more beautiful then I am.
All who are against me must die: this is going too far, so I will just smack them till they cry and no further.
Giving leeways to believers: granting them powers equal to how far they are willing to worship her.

Ishtar thus loses much of her malice. To her, Rin and Ishtar is one, accepting each other willingly and fairly, though she will never admit it outright.

касперский.