Different amplifier class for different music genres?

For example for metal is important to have fast transients, leading edges of electronic instruments to be well reproduced, as well as fast paced and deep bass, while for classical reproduction of the accuracy of the acoustic instruments and super low noise are one the important factors.

Nonsense. The transient on a bass drum, rim shot or cymbal crash is the same in any musical genre.

A system that can make you hold onto your hat in "Another Brick in the Wall" will make you jump behind the divan for 1812 cannon.

A system without super low noise will degrade ALL genre. There must be ZERO HUM and only the slightest thermal rush with an ear on the grill. If you can hear ANY NOISE AT ALL more than a foot from the driver, IT IS WAY TOO MUCH!!!

Most home users would be astounded at how poorly their systems perform compared to good recording studio monitors, typically tri-amped and often with a KW+ per channel. Systems so quiet that you will jump when the music starts!

Here we have Class D subs and woofers, tube mids and tweets for a pikers 615WPC.

"Joe Pass is sitting right THERE!"

So the question is: does the class of the amplifier matter or better suit the type of music you are listening to?

Not at all. The quality of reproduction is what matters and that has a lot to do with execution. No-one has yet sorted out a way to make any kind of audio circuit that favors one genre of music over another; anything you may have heard to the contrary is myth, maybe the most common myth in audio.

NO, a good amplifier will play all music well. My favorite amps are Class A, but run warmer and use more power than Class AB or Class D. In my opinion, Class D sound a bit harsh.

IMHO: At a price point, maybe. If you need a lot of power at a good price, Class D does that. Class A does not. I think matching the amp to the speakers matters more than what you listen to. I had a Class A ARC Classic 60 that was glorious but I missed the oomph of my Moscode 600 Maxi, and I've finally decided (after 50+ years of this hobby) that having enough power matters a whole lot. (At the moment, I have an ARC VT100 driving Vandersteen 5s, but they have built-in powered subwoofers.)
And I think all amplifiers sound the same... until you connect them to speakers.
Good luck, and have fun!

@atmasphere, the most common myth? That might be a tiny stretch. Lets just say one of many:-) 

There is no difference in the power needed to reproduce an orchestral crescendo as there is needed to reproduce Slipknot. A good amplifier speaker match will play anything. You can not talk about the amplifier without talking about the speaker. The two must match. There are amps that will drive anything. They tend to be big expensive bruits. While a SET amp may sound OK on certain very efficient loudspeakers it will die trying to drive Wilsons. An amp is going to sound different depending on the speaker it is driving and a speaker is going to sound different depending on which amp is driving it although there will be some basic characteristics that won't change such as dispersion and imaging.