Well, let's take a look at the problem people have raised it to be and what surrounds it, why it is considered a problem by these and what can be done if something needs to be done:
- It is a problem because the 3-failed-rolls-and-you're-out rule doesn't take the character's resilience into consideration.
- It is a problem because a character at his negative hit point limit can recover as easily as someone at 0 hp.
- It is a problem because the 3-failed-rolls-and-you're-out rule is too random.
That's the opinions I've spotted so far so far in this thread that are construed as "problems" with the 4E way of handling death and dying. Let's then look at what we, as a gaming fanbase, require of the rules, as per the statement of the WotC team:
- They need to be simple, and easy to remember and use.
- They need to confer the feel of fantasy adventure to the gaming table (e.i. keep the mortality relatively low while possible).
And going from this we'll look at the problems now. As it has been said, a character's resilience is already a factor in that the hit points (representation of a character's resilience) determine when this state of dying is reached. Likewise the hit points also determine how likely a character is to simply go unconscious over outright dying when reduced to a given number of hit points below 1.
While hit points are abstract, the new concept of "bloodied" does imply that at some point, the character will know that he's trying his luck or tempting fate. Being bloodied, however, can manifest in many ways, from a drop of blood on your lip or nosebleed to a flesh wound.
And while the abstraction that is hit points seems to treat a character near his negative hit point limit the same way as a character at 0 hit points, there is a difference. First off, the attacks that reduced these sample characters to the state of dying were of different strengths, but only in so far that one attack could have killed a lesser creature while the other couldn't possibly have done anything but render the target unconscious. In that regard there is little difference between, say, -50 and 0. However, the difference becomes apparent with a follow-up attack on the dying characters.
Lastly, the 3-rolls-and-you're-out rule is criticized as random. While that is true, it gives considerably more warning than a simple save-or-die effect. With no failed rolls (yet), you know you have at least 2 rounds to reach the dying character unless someone decides to stab the body.
That brings me to the requirements of the rule: Is it simple? Yes, it is relatively simple and easy to use at the table. That hasn't been contested in this thread, anyway.
Does it inspire heroics and fantasy adventure? Well, the fact that you can roll a 20 to have a miraculous recovery does add a sense of heroics to it, making it possible for someone to stand up and "save the day" despite being down for the count just moments before, while the 3-rolls-and-you're-out creates a sense of urgency in the party if they see a comrade fall, though without causing a panic (since they still have at least 2 rounds). Also, both the chance of recovery and the negative hit point buffer ensure that the heroes, despite their dangerous lifestyle, don't die too easily.
Lastly, what can be done if something needs to be done? This is obviously a simple set of rules to govern the state of dying, mostly appealing to a gamist mindset, and it might not carry the complexity and "realism" analogy a simulationist demands. However, such a complex system could (and probably would) severely slow down the game, making the state of dying undesirable for more than the obvious reasons, or it could - as other posters pointed out - create too heavy an emphasis on some game elements.
In the end, this is a simple rules set that serves the purpose. It doesn't require math or take much time, allowing players to focus on whatever part of the game they wish. Someone wishing for a more complex system is of course free to invent such a system and use it for their game, but with these being the rules intended for the default and core system, they work perfectly well.