I mean, you won't want Bonham drumsounds on a Killswitch Engage album right?
you answered your own question. contemporary music, and i think the same applies to most music, really, calls for specific sounds that may not necessarily sound right with loosely recorded drums. even live, loose sounding drums are a bane for recording engineers or drummers because they can wreck havoc with the mixdown because your frequencies are everywhere, and loosely recorded drums, instead of holding everything together, becomes a liability. as a drummer, this opnion is from personal experience as a performer and production person.
the "Cajon" is not annoying (this is opinion) but a method of giving a recording a different texture without being too overwhelming. acoustic drums with brushes, rutes, mallets or conventional sticks are not ALWAYS the best thing to turn to for all acoustic performances because you have to think about the ambience, the impact, and the composition of the song. you want to treat the resulting recording as a sum of its parts by asking the following questions: what elements would clash if I used these instruments? what choices may i opt for to make them sit better? what instruments can I use to blend everything into a a more cohesive composition? the use of skin dampening is a common practice to alleviate the pain of dealing with highly resonant drum heads live, and n the studio. personally, I prefer using a combined approach of powder coated skins (evans) with gel dampeners while my brother uses powder coated skins with rings depending on the venue because smaller clubs require a shorter decay and quicker attack than bigger places. the differences primarily came about as a result of our different playing styles so we each tried different ways to experiment and eventually settle on what worked best.
so, the take home message is: i don't think natural sounding drums are out of style, in fact, you see this is apparent between records recorded live or in the studio. mixing engineers look for what works with the playing style of the musicians, the context of the recording and the genre of the music material. Since you mentioned "Light Grenades" by Incubus we can use that as an example because with every recording that the band has put out, Mike (Einziger's) guitars have evolved to a more organic sound as he increasingly opts for more vintage pieces over the PRS guitars he has used a lot in the past. To complement this, Jose Pasillas' drums have to sound a bit more focused because it would anchor the playing a bit better. Rage Against the Machine's record 'Evil Empire"was literally recorded live (but tracked simultaneously) while they performed in the live room. Brad Wilk's dynamic drum sound is a great backdrop to Morello's razor sharp and syncopated guitar work. I know Brad uses Zildjian K cymbals live for his heavy cymbal sound which are much thicker than the A Custom's other rock bands use quite a lot.
Just my 2 cents.