The Playstation2 seems to have been a bit of a rush job and not as thought out as what we would have liked! You may be asking why, if so read below.

1- Making it a "Mutimedia machine"
This may be it's biggest selling point, but is it really worth it? The Psx2 costs a lot to produce and Sony sell them for less than it costs to make them and since stats show that a lot of people are buying it as a cheap DVD player, this possibly means that a lot of people may not be buying too many games, which is how Sony make their money (selling games).  The price of the componants will drop in time, but so will the price of the Psx2.

2- The price
Again, by making it a "Multimedia machine" they have pushed up the price, DVD playback and backwards compatibility push up the price heaps! Most people won't spend this amount of money for a "Games machine"

3- Backwards compatibility for controllers
Backwards compatibility for controllers means less controllers sold, which also means less money for Sony, not to mention carrying over some limits from using the same port as psx1.

4- Backwards compatibility for games
We all know how easy Psx games are to pirate, well supporting the same format means psx2 Cd's willbe just as easy to copy if you just get rid of some fmv, enabling it to fit on a cd

5- 2 Controller ports
Sony should know how popular 4-player split screen gaming is! Sure you can get an adapter, but really, this should be defult! Also adding to the $$$ a psx2 owner has to spend!

6- Ram limitations
The ram is very differant to anything else making the psx2 harder to programme for, sure with some effort you can get some good results, but will third party developers really want to spend extra time and money with this if they can make the same game on the X-box or GCube for a lot less effort? One of the reasons the Satern Died!

7- Weak Launch titles
None of the games that were launched with the system were really games that justify buying the system for, sure Tekken Tag is a good game but is it worth the price of the consol? I think not, this has to be one of the weakest line ups ever! All systems before it had at least one game that alone justified buying the system! 
eg:
N64 - Mario, WaveRace & Pilot Wings!
Dreamcast - Sega Rally 2
Satern - Sega Rally and other Sega arcade games.

Sony still have a chance of salvaging this system if they release enough "must have" games, time will tell.