Because it's not the 90s anymore.
Like most things, ads are products of their time. Back in the very late 80s, advertisers thought everything directed towards the youth of America had to be "rad" (things like skateboarding culture and TMNT were huge at the time, after all). Now here comes the 90s, filled with in-your-face attitude that arguably morphed from late-80s "cool/rad"-ness, and advertisers took the ball and ran with it. And what was more in-you-face and filled with totally rad additude than an attack ad showing how cool your own brand is and how lame your competition is? While Nintendo never really felt the need to make attack ads, perhaps because they were a well-established brand and didn't have anything to prove, even they cashed in on the "90s attitude" thing with their "Play it Loud" ad campaign that ran during mid-decade.
But with Nintendo's major competitors, they did have something to prove. By time the Genesis came out in 1989, Nintendo essentially was video gaming, at least in North America and Japan (the only places with large markets for consoles at the time). The Genesis was the first 16-bit system, vastly superior in terms of hardware to the NES, so Sega, existing in the advertising culture of that day, decided that hammering Nintendo's aging-but-still-hugely-popular console would be the best strategy, so they started off by showing how "Genesis does what Nintendon't." Once the SNES was released and they couldn't tout being a next-gen console running against the outdated NES anymore, they simply changed the attacks, positioning themselves as the "cooler" alternative to Nintendo. They would still attack Nintendo on the hardware front as well (see "blast processing" and their Game Gear ads), but the general idea was consistent: be aggressive, be in-your-face, have a lot of "cool" attitude, and tell the youth of America how lame your competition is. And because they were engaged in very close competition with SNES throughout the 16-bit era in the U.S., Sega felt the need to keep up the attack ads.
When PlayStation was a new brand struggling to do well, Sony used the same type of attack ads (e.g., the "Crash Bandicoot at Nintendo HQ" commercial and this notable FFVII magazine ad), because like Sega before them Sony had something to prove. Starting in 1998, PlayStation had clearly established itself as the dominant brand (the PS1 sold roughly 72% more units than the N64 that year in the U.S.), so they likely no longer felt the need to continue the attack ads, hence why they simply disappeared in the very late 90s. Combined with Nintendo never engaging in attack ads and Sega already well on the way out after the Saturn's failure, the practice of attack ads as a primary strategy simply fell out of use. When the Xbox was released in 2001, Microsoft saw fit to not restart the practice, cementing the death of the attack ad in game advertising.
Today, attack ads, especially in the overt style they existed in during the 90s, would be considered gauche. Like I said, they were a product of 80s "totally rad" stylings and 90s "attitude culture" coupled with new console brands that have something to prove. Now the Big Three are all well-established and have been so for a long time, and they have a more or less amicable relationship between themselves. Really, the only thing we see that even remotely resembles the attack ads of old are the occasional little digs here and there, like the "How to Share Games on PS4" video Sony posted on YouTube during E3 2013, but such things are relatively light-hearted and very few and far between. We will never see this industry engage in attack ads in the way Sega, Sony, and certain also-rans did back in the 90s. It's a dead practice, and it's probably never going to be resurrected.
Last edited by Shadow1980 - on 20 October 2019