I could actually think of a way for them to re-boot XCOM as an FPS. It just wouldn't be the way the current developers are doing it:
First, return to the first game's story/setting concept. An elite military force is tasked with saving the world from Aliens and Monsters without pissing off the countries. Set it at the end of 2012 to belatedly jump on the "End of the World" bandwagon, or 2014. Far enough into the future that "It might happen" but still in the present enough to use our weapons and armor. (This retraux 50's bullshit has to go.)
Now, instead of having the player control the entire XCOM faction through the power of Microsoft Excel, have him play a single Sergeant in this faction. Make it a squad-based shooter, with innovative, easy-to-use tactical control and options. Then, throughout the campaign, have several references to the diplomatic and political situation that's going on in the higher echelons of XCOM. The command center or between-mission screens should feature several elements from the older games' strategy interface. Then, even while the game remains a tactical shooter/"Call of Duty meets Independence Day"-type game, it still contains and introduces players to the diplomacy, strategy, tactics, and other elements of the original series.
Also, going about it this way makes it an actual "reboot" of the series, instead of a doomed one-shot that completely kills the series (As the Space-Marine Turok did to that series, without even changing genre!). Future games could have the scope of the game expand towards the original, as the player takes more direct control of the Anti-Alien Task Force as (s)he becomes more familiar with it.
A mental exercise I came up with tried applying the same situation to the Starcraft franchise:
Suppose that Starcraft only gathered a cult following, instead of the massive audience it gained. Also, suppose that Blizzard didn't wait about ten years between games, and instead followed it up with a number of successive RTS games that, while adding more features, just bloated the franchise into an amorphous, corpulent mess threatening to bankrupt Blizzard.
"Starcraft II" is Brood War: Another, completely-seperate RTS with a new interface, splits the three factions into six (Terrans, UED, Overmind's Brood, Kerrigan's Brood, Protoss of Aiur, Dark Templar), and advances the story as Kerrigan becomes Queen ***** of the Universe. It becomes a commercial success, but a few weeks/months after it's release, gamers start feeling that for all it's high points, some of the additions really detracted from the original game. It financially matches the success of the first game, but doesn't acquire the same legacy.
"Starcraft III" Follows shortly after. For the purposes of this mental exercise, it essentially turns the game into what boils down to a Dawn of War clone (but prevents that franchise from forming, keeping Starcraft unique even with the changes. Relic does get into the RTS market with Company of Heroes, though): introducing a Command-and-control economy instead of Alderis shouting "You Require More Vespene Gas", squad-based unit control and production, and a more discriminate, tighter unit cap. Older fans are alienated by the changes, except for a cult few, and new players aren't very interested in it. Still, it's considered a solid game, and some of the older fans who didn't like trying to micromanage large numbers of units consider it the "best" Starcraft game. Story-wise, it focuses on a completely different conflict in the system, using a new cast of characters, kills Kerrigan to restore the faction balance, completely brushes aside fan-favorite characters in favor of new, mostly uninteresting ones such as Nova (A blatant Ghost-Kerrigan clone), Tychus Findley (a grittier, morally ambiguous replacement for Raynor), Praetor Karass, Selendis, and the like that do manage to get their own cult following.
"Starcraft IV" is considered absolute shit. It introduces the Xel'Naga as a playable race, completely bloats the series with new, frequently-malfunctioning features, completely trashes the economy, factions are horribly unbalanced and everyone hates it. And the story is absolutely pretentious shit. Fourth games in a series always end up being shit. Comparisons to Tiberium Twilight and Dawn of War: Soulstorm are apt.
Starcraft IV's abysmall failure almost bankrupts Blizzard... Fortunately, they are saved by taking the MMORPG world by storm with World of Warcraft. Five years later, after several Human Resource shuffles, they decide there's still potential in the Starcraft franchise, as long as they can distance themselves from the third game and fourth games. However, they don't want to pull a Megaman 10 or Sonic 4 by trying to get back to the now-outdated elements of the first game.
Cue Wings of Liberty. Taking inspiration from Starcraft:Ghost, which was canceled in favor of the disasterous Starcraft IV, the game's a first- or third-person hybrid of a Gears of War-type shooter, with sections that wouldn't be out of place in Mech Assault, and a few more space-combat sections with gameplay resembling that of Crimson Skies.
The story reboots after the second game, with a few changes that leave the oldest fans scratching their heads.
In Wings of Liberty, you control Jim Raynor, directly leading the greatly-depleted Raynor's Raiders into battle for tight, squad-based action. A friend can play co-op as fan-favorite Terran Marine Tychus Findley from the third game... though his actual storyline has been completely ret-conned, he's clearly still the same character. The combat is tight and fun, with controls that are familiar to conventional FPS gamers. The game does, however, hint at the original RTS roots of the game. You get a very limited arsenal for the power-armor sections, though. However, this is mitigated by your Gause Rifle believably being able to tear through heavy armor and shred vehicles with sufficient application. General consensus is that the Gauss Rifle may be the only gun, but the way it plays is worth the entire arsenal of Painkiller. And the power-armor sections are just a small portion of the game.
Between missions, you can walk around and explore almost the entire Hyperion... or at least the interesting parts: You can see the vehicles, mechs, and smaller starfighters that you'll eventually get to drive/pilot later in the game. The Wings of Liberty action game definitely feels like Starcraft aesthetically, even with the new vehicles and weapons. However, the strategy, micromanaging, and distant command of the RTS games are replaced with set-piece battles and pre-determined missions. Several of the missions or parts of missions even feel like the commands or situations that pop up in the RTS series... Aside from everything about Raynor and Findley being completely overpowered compared to everyone else to make the game actually playable.
For a complete change of pace, the game even has a section where you play as Zeratul. (Single-player only)
Amazingly, despite the broad spectrum between standard Shooter in Terran Marine power armor, mechanically visceral Mech combat in Vikings, some Armored Awesomeness in Siege Tank columns, and flight-simulator combat in Vikings and other fighter-craft, the game manages to stay cohesive and focused. Despite being such a departure in terms of gameplay from the original series, it's a critical hit.
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That would be the way to update and re-boot a franchise in a new genre.
Not by turning it into a 50's-aesthetic shooter.
EDIT: Why the hell are my tags screwing up?