They probably could do with a striker, but haven't we seen it before where players who perform well for one club move to a bigger club, but is one step too far for them? I can see this ending this way too!
I think your right about Sturridge, who cod actually fall into the category above. He's been at both Man City and Chelsea now and never really worked out in his favour. Maybe Liverpool is his level though (although i cant see him playing as a central striker with Suarez there, and is where he wants to play)