Like it is, a great piece of hardware, $381 to be produced. Try to get more at this price...when it was launched.
Of course, if you choose $450 or $500 to produce it(at Launch), SPECS will be higher, and so on.

Sometimes people seem to forget about cost production and heathing problems.

Improve the CPU. Needs at least 50% more powahh.

I agree that better specs are always better, but improving CPU power implies improving a bit more 'memory bandwidth', so it would cost more to produce it.

PS4 CPU and GPU combined can do so much more than what we have and see now. You will see Uncharted4(AI, physics, animations, collision system, Graphics, sound, everything); and it's just the beginning.   But again, I agree with you, the more power you have, the more is better.

The PS4 has more than enough memory bandwith to have a more powerful CPU. The reason the CPU specifically should be improved is because it's a bottleneck for the rest of the system.

Hardware
- make the PSU external, jeep console size the same and put in bigger/better cooling so
- up the CPU/GPU clocks to 2GHz/1GHz respectively
- Use SATA 3 instead if 2 so SSDs can be fully supported if the user chooses to put them in
- better controller battery life
- make the touchpad a basic monochrome black and white screen, so basically an onscreen keyboard can appear in it for touch typing. The touch keyboards in most phones are smaller than the size of the touchpad so this would work. and when not in a text box other information can appear there all controllabale of course.

Software
- trophy reward points. Basically, every game bought will be worth 10RP. 5RP for all the trophies and another 5RP for the platinum trophy. These points can be used to purchase content on the PS store. 10RP will be equivalent to $10. Give an incentive for people to hold onto their games longer and buy more content from the store.
- Outside the core functions and APIs of the OS will fully open the OS so anyone can make applications to run on it.Think along the lines of how android works

HDMI input, so I can stick my Xbone in it.

Thank god the OP isn't making it. The CELL?! YAY another $600 hard to program machine!

Which would increase cost by a decent amount for like 5% more performance.  Ok paying $450 for that?

I'm actually really impressed with the PS4, I feel some of your goals aren't too realistic.

DS4 - Really good controller, just allow me to charge it while the console is off and give it a longer battery life

Hardware - Rear USB port and non-propitiatory camera lead, so I can actually use mine (the cable isn't long enough)

That's about it. Maybe they could have put more games out there, but I have no idea what's going on behind the scenes. Stuff like the suspend/resume would be good, but what I do want is the ability to change my PSN account date of birth and location...

Sorry to say but your ideas really are not good, for the simple reason that your imagined PS4 is expensive. You also come up with complicated plans as well.

1st off: You just assume the Cell cpu has become twice as cheap, it probably hasn't considering the PS3 didn't get much price cut since 2009. The basic version should cost less than 150 euro by now but it's still above 200 euros.  And then again, $20 added BoM cost that's eating away from their profit is too much to please an awfully small group of people on the internet begging for BC. BC really isn't the reason people buy new consoles, and they knew they had PS Now coming. Any effort to BC is just wasted.

2nd: glad you didn't design the PS4 because you just continue to make the console more expensive.One thing I agree is that they should've clocked the cpu higher, the gpu is good as it is but it seems to be bottlenecked by the cpu.

3rd: here comes the confusing part. Who the hel in their mind would allow multiplayer in a free subscription when 95% of the people who signed up for PS+ did for multiplayer? Your plan just make it overly complicated and try to persuade people to sign up with far lesser reasons. The vast majority doesnt care about the ads or 10GB cloud storage or having unlimited friends or having 12 accounts. WTF? They care about their multiplayer. PS+ would not have 1/10th the subs it does today. What you just proposed was a really terrible idea and really one of a gamer on a forum mind rather than someone who is running a business.

4th: again, they didnt need to waste 10s of millions of dollars for a better exclusive support. 20M bought the console without the support anyway. You just put all of Sony studios effort in the 1st and 2nd years, congrats, in this age where big AAA games take +3-4 years to make, you have nothing left for 2016 and onwards. On top of that, you assume you have money left and spent that money to get 3rd party games exclusive in a period when 3rd parties where predicting the xbone to win. Back when Titanfall was being conceived EA was betting on Xbox. FFXV went multiplat for a reason, they didnt believe in the PS4, getting those titles exclusive if they were conceived today would've been far more cheaper. SFV is a recent project, Capcom saw PS4s sales,  calculated they didnt need a second console for the game to reach its audience and accepted Sony's offer.

I agree with you about GT6 however, it has been worked on since GT5s release in 2010, had they continued to work on it for 2 more years and made it PS4 exclusive, it'd come out this holiday.

Wit the 1st and 2nd points Sony might've still greenlit your idea, with the 3rd and 4th points they would fire you in a week.