Keywords in text - an idea (?)

..hope I am not beating a dead horse...

[Hard_Target]

You may or may not agree that a good sales copy text is typically quite different from SE friendly text, but for sake of argument let's just assume that it is.

How would you evaluate the idea below in terms of
(a) SEO value (i.e. beneficial, harmful, irrelevant) and (b) conversion rate (i.e. no effect , harmful)

On the bottom of (home / each / dedicated -take your pick) page, below the fold, below everything you want your user to read, place the following (no hidden text, no small print, no other tricks):
The users of #*$! (whatever the site is about) accessed our site by using the following search phrases:
(The list of actual phrases from the logs, mixed with phrases you would actually want the users to use follows, and is changed as frequently as practical)

[mona]

I don't think it's a bad idea, actually. Assuming you're not planning on over doing it;)

> (a) SEO value
I can see some value there for multi-word, non-competitive phrases.

> (b) conversion rate
The way your planning on doing this, I can't really see it effecting conversion in any way.

[Algebrator]

That sounds interesting - what would be "overdoing it"?

[mona]

A big, long list of KW phrases that might draw the attention of the user. It would look tacky and sorta spammy, don't you think?