1 CONCORDdoesn't have titans, mostly because CONCORD only operates in the "high security" area of space, where capital ships are not allowed and jamming fields keep their drives from operating. Of course, since it's CONCORD defining that "high security" and maintaining those fields, they could presumably have titans if they wanted them. But since they have insanely powerful ships made if GMium, it hardly matters.
But it's irrelevant, you can't set "take on CONCORD" as a goal for an alliance. Not only do alliances and CONCORD operate in entirely different regions, but fighting CONCORD and not losing your ship is considered an exploit and can cost you your account.

2 Then what else do they do?

3 In the past, when a coalition has gotten so big that people start tearing their hair out about nobody being able to face them, it falls apart pretty quickly.  A lot of the people in charge of big alliances have pretty abrasive personalities and histories with each other.  And of course, enough people are in the game just for the pleasure of blowing each other's stuff up that they're not going to stay allied for long if that means there are no targets.

4 If memory recalls, the last time one corp alliance got big enough to dominate the game, the Goonswarm sent in a mole - in two years, the guy worked his way up to the alliance's chief financial officer. Said mole then waited until just before the "rent" needed to maintain system sovereignty was due... and then completely emptied out the account responsible for paying it. Something like a third of the systems that could be controlled missed their rent payment and became uncontrolled all at once. (Think of it like every "client corporation" going to work only to find padlocks on all of the doors, with most of their capital assets on the other side of those doors...)

Chaos ensued. Reading through the article, the flash point of the battle there was a single unpaid sov bill. With hundreds of systems up for grabs at once...

The thing is, the sov is owned by the alliance, but almost every actual facility and vessel is a member of one or another of the subsidiary corporations. If people get bored, or tired of paying rent, they do have the option of picking up and moving elsewhere... though of course the main alliance can turn on them and try to prevent their defection. But if they represent a significant fraction of your supercapital fleet...

(The converse is that the corps who do the grunt work back in the conquered territories get fed up paying rent to the big guys who spend all their time pewpew-ing on the other side of the galaxy, especially if that means you don't have enough combat pilots at home to protect the vulnerable miners and transports from opportunistic raiders. Enough of these guys bolt, and suddenly you don't have the economic base to keep up the war effort. But it's hard to convince people to play security guard while you go have all the fun.)

5 This is why I love to read about EVE, but I don't play it. I love reading well reported stories on the events in game. It's like an amazing piece of sci-fi writing.

6 As one of the commentators said, it wasn't a complete rout. CFC had to ally with the Russians, and they lost 16 Titans of their own.

OT: Some of the World of Tanks articles on that site are interesting if you liked Yukari's tank corner on Girls und Panzer. One was on Japanese tank development (which explains why there aren't any WWII Japanese models on the show), and another was on why the M4A3E2 Sherman Jumbo was popular in WWII but not in tank-on-tank battles such as in WoT and presumably senshado (although that might change if it's equipped with the 105mm howitzer).

7 There were two Japanese tanks in the show: Duck Team's Type 89, and Anteater's Type 3.

8 I forgot about them, but they definitely took a backseat behind the main characters' Panzer and even Hippo's Sturmgeschutz and Rabbit's M3 Lee.
The GuP production team collaborated with World of Tanks Asia on a beginner's guide to the game. (Nishi Kinue, the unseen leader of Chi-ha-tan Academy which was crushed by Maho in Ep. 6, is in the panel on Chinese tanks.)
Can online games like EVE and WoT provide the team cohesiveness feeling that you wrote about here? The player wouldn't be a component like in senshado since he controls an entire tank instead of being a crew member, but a team clicking like the SEALs might be possible.