"Remaking the game on fresh technology would be expensive; even with the current console generation... ...With the current online gaming scene dominated by Modern Warfare, Gears of War and Halo 3, it's pretty clear that tastes have moved away from the "bouncy deathmatch" model of the Quake series."
I don't really care about consoles--hand controllers will probably never compete with PCs in terms of raw playability compared to a mouse and keyboard. As to the expense, we're talking about massive savings using the existing game design. A graphical upgrade wouldn't be cheap, but I doubt it would be prohibitively expensive. Compare it to developing new games, or (more relevantly) developing and adapting an 11 year old game and paying for all the infrastructure to centralize the servers, etc in Quake Live.
People's "tastes" are not confined to one variety of gameplay. The games you listed are the current wave of mostly-console hit FPSes. They are slower games with heavier physics and a multiplayer emphasis on team strategy. They work best on a console because the slower, more cautious gameplay suits the less agile controls better. A PC with better controls fits best with a different type of FPS experience, and currently, I see no example that beats Quake 3 for that type of controls.
"despite the strong support it gets from part of the fanbase, Quake 3 perhaps had less impact as a game (as opposed to its engine, which powered umpteen other games over the next few years) than had been expected. With its multiplayer-only focus, its emphasis on the "pro-gamer" market and its lack of new ideas, it really marked the point where id lost their leadership in the fps market."
I really just don't understand this. Quake 3 Arena was seen as a resounding success and essentially set the standard for a multiplayer FPS to beat for many many years. I don't think it caused Id to lose "their leadership in the fps market," except for the fact that, as I would agree, they didn't update it fast enough and eventually people were wooed by the "new" games. In my experience, the community was large, easily accessible, and persistent. For years I played sporadically, and saw hundreds of servers each time I looked for a game. I almost never saw the same people, unless I frequented a particular server, and then only sporadically.
I also don't understand why "multiplayer focus" is an irreducible problem with the game. Just because people are playing single player console games now doesn't mean that is a superior game type. Quake 3 Arena simply is not Quake 3 Arena when you turn it into Gears of War or Halo 3.
"It's not really age that killed the game off from the tournament scene, but rather the fact that the audience shrank relatively quickly."
Quake 3 had an active, reliable, and large audience online for an extremely long time. It was released in 1999, and there were still many major tournaments with a broad and high level of players in 2006. I don't understand how that translates to "relatively quickly."