Why not charging battery on wifi signal?

I just became aware of this nice piece of video made on CES 2010.

They argue that batteries of cellphones and similar devices can be recharged by solely relying on power emitted by wifi hotspots. In fact for me this is somewhat hard to believe so let's make some calculations:

First, let's assume that the efficiency of the device is 100%, meaning that all received signal is converted to battery power (this is quite optimistic, since charging up a battery usually worse than 70%). Anyhow, if we have a single cell LiIon battery of 1500mAh, that will need approximately 1.5Ah*3.7V=5.55Wh energy input to be charged up completely.

Now let's see the other side of the equation: According to this howto page, the maximum transmitted power of a wifi hotspot can be 1W. This itself would be sufficient if we can catch everything, our battery is charged up in 5.55 hours. In fact, usually this is not the case (luckily for others, because they still would like to use wifi as it is intended :) ). For me it seems, that the size of the device is around 5cm × 10cm, giving an area of 50cm^2. You can measure this for example at 2:24 in the video above, where you have the hand of the guy for comparison. In this case, if we are 1m away from the access point, then this 1W goes through an area of 12.5m^2 (simply assuming that it the pattern isotrop), meaning that we catch 0.005/12.5=0.0004 part of the transmitted power. This is 0.04%! Anyhow, we get a power input of 0.4mW, so the time we need to charge up the battery above will be:

5.55Wh/0.0004W = 13875h = 578 days = 1.6 years.

I think I have been quite generous with the approximations above, so this might be some sort of best case scenario :) In fact, if go further away from the access point, the power input will cut off with the second power of the distance, and also the power conversion can add a factor of at least two.

I anyhow wish good luck for every end users so that they can make a single charge once every elections :)