Its not out of the question at all, my point (poorly made), is that LAMP costs $35, the reasoning is like this:

LAMP - Linux-Apache-MySQL-PHP, requires Linux which moves you into a memory managed core, Apache+MySQL adds memory requirements this puts you at 256MB minimum, 512M better 1G ideal. MySQL+PHP adds storage requirements (they are reasonably moot because an SD card can have 32G no problem). So the system requirements of the software, raise the cost of the hardware. If you buy that hardware in onesies quantity will cost you $50 - $75, if you can buy it in huge quantities its less, the RpI distributors can sell it for $35 but no idea what sort of margins they are getting.

Requiring LAMP is a "skills" play, which is to say it costs less to find a skilled programmer who can code inside a LAMP infrastructure than it is to find one who can code in an embedded infrastructure. That can decrease your time to market and your development costs. From a business perspective one would look at the total cost of developing the product and then the lifetime value at a given price. If you know that you over payed on the Hardware to get the skills advantage, then if you were doing a threat assessment to your market (part of a SWOT) you would note that someone who did it with an embedded programmer could come in and undercut your price and still make a good margin on units sold. This is exactly what Network Appliance did in the NFS server market, they ported NFS to the bare metal and sold a box based on the 486 that out performed a Sun 4 server at 1/10th the cost.

So if you are only making a few, the question is silly, $25 or $100 dollars won't make a big difference and there are lots off off the self solutions at the high end of the price range (PogoPlug, Guruplug, Etc, Marvell's whole effort there) If you have an on going market though, getting better margins per system pays off the longer you sell these things. You can compute the cross-over point with simple math based on salary of programmer, cost of goods, gross margin of the product.

Just saying "I want a $25 system that is LAMP based" is like saying "I want a car that costs what every other car costs except that it can fly." Which is to say, its a whine. You can also reason to a pretty good guess that a $25 LAMP system doesn't exist but looking around at Hacker News or a variety of tech themed web sites, You have no doubt seen all the press RpI got, and if you went back in time you could see the press the Dallas Semiconductor Tini (single chip web server) got, so you could reason that any LAMP capable system at that price point would hit all of the tech sites like a ton of bricks. It would take effort for it not to create a lot of news. So you can be reasonably certain it doesn't exist.

Now if you want to know why it doesn't exist, well you can figure that out too, take the Linux kernel and the efforts that have gone on to put it into small ARM chips, (there are lots to choose from) and look for the minimum viable chip to run Linux, then go to the manufacturer's web site and look at pricing (or use Octopart if its in general distribution). Look at the 1K price (that is "if you buy 1000 units") because it will be the nominal "street" price of the chip. Now price memory chips, ethernet magnetics, and board design/build. The PCB is going to cost $1 - $3 each depending most of these you can do in 2 layers but some designs really need 4 layers because the pin pitch is so dense. Then you'll want to find a place to make them. I'm lucky because living in the Bay Area I've got my choice of over a dozen shops that can make and assemble fine pitch printed circuit boards as a service if you're just making a hundred or so. When your run that exercise (at least when I do) I come up with between $35 - $40 per unit at about 1K units. Which, if I were to sell one to you I'd probably sell for between $75 and $150 depending on whether or not you were planning to resell them. To test my math I would go out and see if there were any products in that price range, and would find this one: http://www.adafruit.com/products/278 the 'chumby hacker board' which retails from AdaFruit for $89.

And then I would feel confident in asserting that no $25 system yet exists that supports a LAMP stack.