It's not a no brainer at all. Whilst I agree the £20m fee, in this market at least, is not an enormous outlay the £6m a year for at least 3 years (but probably 4) is given our turnover.
For what it's worth I think it is probably worth the risk as we are desperate for pace and goals (although he won't score anywhere near as many here as at Arsenal because of the differences in style of play and personnel).
I think we view risk differently however as when we were discussing Martina prior to his signing you said the following:
Good vaulting
FWIW on Martina, am I wrong?
Clearly, I was wrong on how Koeman wanted to use him and Kenny, but in terms of how it's worked out Martina has been providing cover in numerous positions and for all of his faults (of which there are plenty), he's been an ever-present as we've improved defensively.
Now that's not down to him and simply put he's nowhere near good enough, but ironically enough if we hadn't brought him in we'd have been in an even worse state at the back personnel wise due to the injuries.
I agree entirely on your points about Walcott, btw.
I'd say it's a no-brainer though in terms of getting someone proven in the league who can score goals - as you say, probably not as much here due to styles of play etc, and creates danger because of his pace, which is something we've all bemoaned the lackof so far this year.