Rogue - you are partially correct.
Believe it or not heavy metal actually stole from Jazz, Progressive Rock and Disco when it came to set size.
Anyone not interested in drum history tune away now, this is long and boring.
The drum set is actually the Frankenstein creation of the old theater musicians of the early 1900s. When silent film and Vaudeville were the standard, kits were used not only for rhythmic purposes but also for sound effects (which by the way is how the hi-hat was invented, it was originally a sound effect, not a real instrument) Tom-toms were Chinese or Native American in make and were "tacked" on in order to reproduce an array of sounds; before this all percussion was orchestra style.
Ludwig, Slingerland & Leedy (in the US), and Premier (UK) were some of the very first companies to introduce "Jazz" kits or drumsets. The usually consisted of a bass drum, a snare, a floor tom and mounted tom and an array of cymbals that varied by performer but almost certainly included a ride, a crash and a hi-hat. Eventually by the 40s the 'standard' five piece (two mounted toms) was almost as common as the four piece.
In the late 50s/early 60s the four and five piece Jazz combo was the standard though a few jazz pioneers (namely Gene Kruppa and Buddy Rich) began to experiment with adding an extra bass drum or another floor tom. Though rock was still using the 'traditional' kit, changes were already happening.
Rock drummers that notably broke the 4/5 mold were Ginger Baker of Cream (who used 2 basses or kicks, 2 floor toms and three mounted toms), Keith "the Loon" Moon of the Who (who supposedly had all those drums so he wouldn't miss) and Carl Palmer of ELP who added so many orchestral instruments to his traditional kit that he looked like a one-man circus when he preformed lived (and along with Emerson's keyboards along the back wall... you get the picture.) Likewise, the amount of cymbals these guys used started to break the standard three mold as well. Though not pivotal in name the group Iron Butterfly's hit "Ina-goda-da-vida" with its 3 minute drum solo in the middle set the tone for more drums equals better sound.
By the time the 70s came around most all drummers had 7 to 10 piece kits, even for the most simple music, part of it was the show of course, but drummers were beginning to be released from the mold of 2 & 4 and providing the backbeat. Progressive groups like Rush, Kansas and the like needed all that 'firepower' in order to open the musical envelope while veteran groups like the Grateful Dead used a two drummer attack with a dizzying array of percussion from all over the world during this time period. Disco drummers were also trying to get more sound for the pound and acts like Earth, Wind and Fire and ELO were sporting the monster kits as well. To compensate the drum companies all had 7 - 9 piece kits listed in their catalogs as well as a large selection of add on drums to make really impressive kits.
Of course as Rogue mentioned KISS played a big part as well, Peter Criss couldn't match the on stage theatrics of his fellow members so his drum riser got larger and larger and eventually became a mobile weapons platform for the band's pyrotechnic show. In the 80s Heavy Metal was very much about bigger is better and many groups felt this meant drums as well as stage shows (ala KISS). The most notorious example was Luis Cardenas who sported a monster 75 piece kit painted in tiger stripes. This was the largest single drum kit at the time and though it has been 'officially' (see note below) been beaten in the Guinness book of World Records in my mind stands as the single largest kit ever created for continuous play.
One of the problems with these kits is of course the tremendous amount of time and dedication it takes to set them up, get them set just right and still be able to have the drummer hit stuff. The CAGE by TAMA, a rack system that allowed the drummer to build up as well as around, enveloped the drummer allowing them to surround themselves and still function is perhaps the pinnacle of basic technology created for the drumset, however it was the invention and eventual improvement of the electronic kit that eventually started the Preparation-H like shrinkage of the over-sized kit hemorrhoid.
Neil Peart was the ambassador of electronics when he in 1988 threw half of his kit away and integrated a wide array of electronic triggers to still have the sounds he craved but without having to have a single tractor trailer haul around his drum kit for tours. This came after seeing smaller jazz players like Peter Erskine and Billy Cobham integrate electronics into their normal sets but only for the purpose of electronic sounds.
The killer came in the 90s when grunge killed the large drumset (like it killed so many other things in music). 4 piece kits became the norm and often the drummer was once again relegated to 2 & 4 with no fills.
As an aside, many drummers are much better on smaller kits, especially if that's what they are used to, their solos and fills are much more musical and inventive, however when faced with a drummer who has command of a larger kit and its intricacies, they just can't keep up.
BTW I play a ghosted 9 pieces (an 8 piece with a double-pedal and several electronics thrown in for good measure - viva la grandiose)
**** Luis Cardenas was replaced as having the largest kit when Chad Smith in conjunction with a Drum Store assembled a massive 129 piece kit for him to play. He did play it, but only once and the kit was just a bunch of 5 and 6 piece sets that they put side by side and then sold off as individual set to fans as a publicity stunt to sell drums. This in my book is cheap, especially since Luis' kit was custom built and with a few exceptions (like the kicks and the dual snares) did NOT have a single replicated piece in the count. He will always in my mind, at least until a real drummer that can back it up and put it out on the road, will always hold that record. ****
So, does that answer your questions?
Thunderfoot, bringing the thunder since 1970...something..