Searchengines can't tell whether a logo is nice or not and thus send more traffic to a site with a nicer logo
Logos have no influence on how searchengines operate thus they do not, in any way shape or form increase traffic to a website = FACT.
Oh dear, this is getting a bit silly, is it not? Who said anything about search engines? You need to look at this from a wider perspective.
If a company's logo has no influence on their bottom line why spend money on a logo at all? Why don't we all just write our company names in Helvetica or Times Roman?
A logo, together with all the other brand elements, conveys a certain message and it is this message that influences conversion rates. The logo plays its role.
As for logos helping people stay longer on a page...can't say I've ever been influenced by one...and I have never seen any research to suggest logos increase conversions...and I've looked. Unless you can come up with some research confirming logos improve conversions there's no reason to believe or suspect they do given that logically there is no reason why they would.
There are a LOT of things that are completely outside our awareness that influences our decision making so it is understandable that you can't say you've ever been influenced by a logo to stay on a site longer. That does not mean the influence is not there.
The F-Shaped pattern for reading web content, Google's Golden Triangle, the effect of partial content above the fold on encouraging users to explore the content below the fold, the effective use of colour, use of negative space in web design, etc, etc are all example of influences that we are not directly aware of.
A data example on these influences are from Jared Spool, who wrote about a case on how removing a button and adding a clear error message to avoid user errors in a checkout process increased revenue by $300 million in just a year
Another well known case study is of how revising their error page so that it contained useful help text improved completed checkouts by 0.5% per month.
The above two examples are inside the interactive decision making pipeline so they are different from the visual influences but I mention them to illustrate the point of how much we are influences by things we are not directly aware of.
The logo, layout, design elements, colour, ect. all falls into the category of the overall impression created by the site. They create things like a sense of trust, positiveness, stability, desire, approachability, etc. and these all influence how long we stay on the site and how likely we are to convert from a visitor to a customer.
That, at least, is why I design logos.