Tube amps distort the sound more, and clip more gradually. This basically means that a digital amplifier can perfectly emulate a vacuum tube amplifier as long as you aren't maxing out the range and clipping the digital amplifier. (You may need a slightly higher rating on the digital amplifier to achieve the same volume.)
I used to have a Marshall JCM 2000 Dual Super Lead, that thing sounded amazing.
Absolutely not impossible. If you can define it you can design it.
Not impossible. Hard, expensive, or currently not available but not impossible.
Class A uses tubes, and works in the simplest and most accurate way by amplifying the complete signal. It maintains the most important characteristic needed to perfection - linearity of waveform amplification. When you try and get extra juice out of it, instead of the annoying clipping you get from digital amplification, you get a nicer sounding and more gradual reaction. The main drawback is energy efficiency. There's a theoretical peak efficiency of 50% to Class A amps, and what's worse is that it's usually less than half that. It makes tube amps that aren't small require massive heat sinks, and increases the BOM.
Class D is totally different. It dumps linearity out the window in favor of energy efficiency. It basically outputs a bunch of pulses, and then applies a low-pass filter to remove the annoying artifacts. While you might say that it's close enough - it isn't for high fidelity systems, especially in production studios, live performance, and audiophile cases. While competitive in quality with the low end of amplifiers (under $200), if you are looking for accurate detail reproduction there is no replacing linear amplification yet. The advantage is that even at the worst use scenarios, Class D amps have over 50% energy efficiency, and usually manage over 90% for higher volumes, making them need far less in the way of heat sinks which allows for leaner designs, and a better price/performance ratio.
The Class D amps will eventually win out. Class A amps have decades of R&D as an advantage, but Class D is improving by leaps and bounds. Eventually, Class D will become "good enough" and replace Class A altogether because of the advantages in price and energy efficiency. But that day has not yet come.
That being said, I use a class D amp for my home set up. It's close enough, and my power bill thanks me monthly.
Class A amplifiers can be made in solid state as well, very easily. As a truly simple, DIY example: http://headwize.com/?page_id=31
There's nothing about solid state that requires a circuit that "outputs a bunch of pulses, and then applies a low-pass filter" -- true linear amplification exists in the transistor domain just as well.
And even if solid state did require quantization (beyond the shot noise that vacuum tubes suffer from also), given that we can do direct digital synthesis up to the 100's of MHz regime pretty easily these days (i.e. beyond the bandwidth of most audio tube amplifiers), with 24+ bits of resolution, there's no reason that a solid DSP system couldn't emulate a vacuum tube response well enough to be electrically indistinguishable from the actual tube.
But, as the grandparent post notes, it's one heck of a lot easier/cheaper to just use vacuum tubes. Which is why I'm staring at a tube-based headphone amplifier on my desk right now. Though it does use solid state buffers, which incidentally are way more linear than the typical ways -- capacitors, transformers, etc. -- of removing the DC offset inherent to tubes...
Personally I like Class D amps for basic uses like computer speakers and such. That said, I have a very basic class D receiver/amp that I use as a preamp for a larger 2.1 system with studio monitors for computer sound, as I like my FPS games and music to be clear and accurate while still being loud enough to "feel" things like explosions or timpanis.
Technically the Class D amp can push those monitors well enough, but at more than 1/3 volume there is some distortion and clipping, whereas on my discrete amp I have yet to find any distortion within comfortable listening levels.
But I only have 22 years experience playing guitar and bass across genres as diverse as jazz, blues, gospel, metal, modern rock, and folk, so hey what do I know?
They are doing that to save costs: real tube amplifiers continue to be posed as higher end at higher prices.
A decently modeling amplifier would probably need several hundred watts, if not into the thousands, just to replicate a 50W tube combo at volume. The speaker cabinet and drivers would have to be different: high fidelity units, not guitar speakers.
I think people do get good results when they plug their modern amp modeling digital signal processors directly into a loud PA system, where the models find a decent amount of headroom and fidelity to reproduce what they are doing at loud volume.
If you just want "interesting noises" the VST plugin FuncShaper from Met-RS works great for adding distortion. It's a lifesaver on direct bass tracks. Pipe that thru a convolution of a good impulse response from a nice amp and you can't tell the difference easily.
Because decades ago we simply didn't have the processing power to that kind of DSP.
Today, however, you carry that kind of processing power in your pocket.
It used to be really hard, because (amongst other things) the oversampling required to avoid digital aliasing. This is not really a big deal anymore, today. Also, it so happens to be the kind of calculation that parallelises very nicely.
I can really recommend this video to dispel the myths about what we supposedly can't to today in the digital domain: http://xiph.org/video/vid2.shtml (the guy also presents the matter really well, I found it very enjoyable to watch, even if I already knew over half the things he explains). To really make his case, he feeds signals to both a digital and an analogue frequency analyser.
As a related illustration of the idea, it is common to see microphones in front of small tube amplifiers, which then feed into a large PA system. The small amplifier acts as the "signal processor" which produces the tone, and the PA just makes it bigger. It has the headroom to do that.
In that scenario, the tube amplifier with a microphone in front of it can be replaced by digital modeling: something which produces the same transfer function as what occurs between the signal from the instrument, and the signal going into the console's microphone input.
[1] http://en.wikipedia.org/wiki/Class_T_amplifier
[2] http://spectrum.ieee.org/semiconductors/processors/25-microc...