|Not a joke|
Trebor Daehdoow covers the thing here. EVE combat is O(N^2) in the number of pilots involved. So no matter how much processing power you have, linear increases in N will always exceed the processing power available. (We hope that Moore's Law overcomes this, but it has not in the past few years.) In short, "Fleets expand to fill the lag available".
Daehdoow covers the three ways in which CCP can address the problem: more hardware, more programming effort, and changed mechanics so that too-huge fights don't happen. Of these, they are already maxxed out in hardware, and programming effort has already been heroic. The low hanging fruit is already harvested.
Anyway, all that is prefatory to my idea for how to fix the problem. And that is: remove ships from the field when TIDI gets high. One might be "nice" about doing that; perhaps a forced logoff with a cooling off time allowing no login. But then it is hard to think of a rationale for why ships would just disappear in the middle of a fight. It's a huge fight: they want to be there! And also, this is EVE: if you want something removed, kill it.
I thought about the idea of using player-controlled weapons to create such an effect. For example, perhaps a giant area-effect weapon of some kind. But I think this is a bad idea. You want the effect to be guaranteed by the server, not the players, regardless of whether the players like or want it.
So, I propose a new mechanic. When a particular server is sufficiently overloaded -- let us say, below 20% TIDI -- then there is a chance of a very damaging area-effect explosion. Our bullshit scifi explanation might be: due to the massive energy of large fleet combat, there is a rip in the space-time continuum.
The chance for a space-time rip to happen should increase with increasing lag; for example, it might be 1% per hour at TIDI 20, then double for every point lower, so that at 10% TIDI it becomes 1% per each 7 seconds or so. (This gives an average time for a rip to start of about a minute.) When a rip starts, there should be some warning, such that smaller ships might be able to warp off grid. And there needs to be a epicenter, which should be computed as the center of mass of all ships on grid. So, put an cool graphic there, a pulsing nastily energetic looking thing. Or maybe a black hole looking thing. Whatever it is, make sure a warning is popped up to everyone. Indeed: put a marker on the system map, like a cyno.
One minute after a rip is created, it explodes and vanishes. The explosion does damage directly to shields, armor, and structure of all ships on grid. The amount should not be mitigated by speed, but only (a) signature, and (b) distance from the rip location. This needs to be carefully tuned, but the idea should be that even a distant, undamaged ship should be at mild danger (say, 5%) of being blown up. Ships right on the rip when it tears should die fairly reliably. All other ships should take substantial damage, including hull damage. The armor and/or shields would be reparable in short order with the sort of logistics that fleets have, but not hull, which would make it increasingly deadly to stay on grid after a series of rips.
Thus, below 20% TIDI a large fleet battle becomes something of a game of chicken. Both sides still benefit from having a larger blob, but proportionately nowhere near as much, since both sides will be taking more or less constant (and equal) attrition. In the limit, a large force that simply gets on grid together with no enemy ships present whatsoever would create risk for itself; basically any large fleet which causes TIDI is punished. FCs would learn not to do that. They'd do it only on the field of combat.
A massive null fleet battle would then have a strong reason for reserves, rather than simply throwing in all force available immediately.