Reason to be beseigin'? They don't need one- societies run by megalomaniac dictatorships bent on world conquest (well, all of the world within reach, anyway) have only one purpose- to own everything in sight and conquer any competitors. And Vegas with its dam is the perfect place for Caesar to build his 'Rome', with plenty of electricity and slaves handy. Whether or not the NCR is corrupt, wicked, weak, or a bunch of perfect angels, doesn't matter- they are there, so they are Legion-fodder. Any evil dictatorship worth its salt has to have an Enemy #1 against which to aim their propaganda, and to rattle thier sabers at to get the troops all riled up. The NCR fills the bill nicely. It isn't about whether the area is already stable or not, or could easily be made so by the powers already in place- Caesar could care less about any of that. It's about conquest, baby! It's about ideology and power, not the happiness and comfort of the people in the target zone.
Now, as for how he goes about it, that is pretty stupid. Only a fool (and presumably Caesar isn't supposed to be one) would make their main attack a frontal one against a heavily defended dam. All they would have to do is make a show there to hold the main NCR force, while sending the bulk of their Legions across the river at Cottonwood Cove and such, and swing north through Novac and maybe a secondary force through Primm/Sloan. There aren't any significant bottlenecks guarding the Novac approach route, so the NCR army would have to face the superior Legion numbers out in the open. Game over. Also, that move would cut off the NCR supply route through Camp Mojave. And when this flanking attack forced the NCR to pull most of their troops off of the Dam to confront it... well, things would be lookin bleak all over for the brown troopers.
Dividing one's troops in the face of superior numbers is about the
worst thing a commander can do unless his opposite number is totally incompetent, which General Oliver is not. Paralyzed by indecision, yes, but not incompetent (remember, he svckered the Legion into a trap and trashed them the last time the two sides fought). The NCR has multiple outposts within sight of the Colorado river which would detect any attempt to move a large enough force to make a flanking maneuver worth bothering with, at which point Oliver would send all those Rangers and Heavy troops at the dam across to assault the now (greatly) reduced Legion force under Lanius, which would result in the flanking force itself being flanked and the NCR having a large body of troops right next to Caesar's HQ.
You see, the thing about a show of force is that it's done with a relatively small number of soldiers, as the idea is to make the enemy commander think that your main force is still there and coming for him when it's actually elsewhere attempting to either surround him or cut him off, as applicable. The problem with attempting such tactics here is that both banks of the river at this point are sheer cliffs aside from Cottonwood Cove and Deathclaw Promontory, and as such there are only a couple of places any landing could possibly be made. Since that is the case it's fairly easy to predict where the Legion would pop up at, and those locations are themselves surrounded by cliffs until you get inland. It's true there are no bottlenecks around, say, Novac, but the Legion troops would have to get that far first, and there are only a couple of routes by which this could be done which are themselves readily sealed off given the advance warning the riverside outposts will deliver. Hell, the area between Camp Forlorn Hope and Nelson is already heavily mined by both sides, since they realize that it's the only viable way to get to or from the river landing down the hill.
Since Caesar sees New Vegas as his 'Rome', it is by definition the 'right' place to be besieging, however he's going the wrong way about doing so. Rather than committing to a frontal assault on what is likely
the best-fortified location within 500 miles he should have taken his troops far North or South of it and attacked it indirectly by forcing the NCR to react to his maneuvers by shifting their troops to a more exposed location where the Legion's mobility advantage can be exploited for all it's worth. Contrast this with an assault across the top of the dam, which is a sniper's paradise; with sufficient ammunition a handful of NCR Veteran troopers could hold it against hundreds of times their numbers by holing up in the towers and blasting anything that moves. Of course, in practice that doesn't actually work since the Legion figured out that the intake pipes were not being watched, but in terms of tactical assessment it's exactly what would happen.