Oh yeah forgot about have to write the shooter and Person shot, cant believe Id over look something like that
Anyways, as for Rem, she was a very valuable asset, She was the only shinigami on earth and one of only 2 Shinigamis shown in the series that actually gave a shit about what happened to a human (teh first one being Jealous). The other Shinigami both in the Shini relm and the Earth Relm were only there either because there book got "accidentally dropped" and just wanted to have some fun by starting the train of chaos (Ryuks case) or just because there Book got stolen (Sidoh 's case)
Even in the Shini relm, you would see the Shinigamis playing cards to kill sometime and watching the chaos in the human world to laugh at it.
Rem(and jealous) were the only one who cared about any human what so ever.
As for Rems personality, lets compare it to Ryuks personality just to see how valuble Rem really was
Rem Informed Misa about all the rules and regulations of the death note thoroughly and actually gave jealous's Note book to Misa.
Ryuk just Kinda informed Light about the basics, and let him figure out the details himself.
Rem was on Misa's side, she was on earth only for the protection of Misa. Ryuk was on earth to have some fun.
Rem firmly stated She is on Misa's side while ryuk firmly state that he is on no side at all and was just there to observe/kill time
Rem Helped Misa in every way possible, including showing her who the Third Kira (that youtsuba guy I believe) was, even when Misa had no longer the Death Note in here possession.
Ryuk only told Light that he was followed by penber because Ruyk dident feel comfortable.
Rem Died For Misa
Ryuk killed LightSo as you can see, there are vast differences between Rem and Ruyk. Ryuk was just an observer while Rem was actively working to support Misa.
Now, having a Shinigami on your side with the ability to see everyone's name and life span, phase threw walls, not bee seen by anyone else but rems DN holder who also genuinely cares about you and has made protecting you the sole reason for there existence is much better then having a Shinighami who gives you as little information as possible, Distracts you on purpose (if there's nothing in it for him) and dose not give 2 Shits about you.
Thus we can conclude that Rem, was indeed a very, very valuable asset.