Part of the reason that the NCR is the biggest game in town is that they had the economic engine of The Hub to drive their growth, and it stands to reason that they were one of the largest and earliest-established trade settlements of that nature for hundreds of miles around. Even as society was just beginning to reform itself, The Hub merchants were a pretty big deal, and their caravans probably covered more of the wasteland than just about anyone else had a reason to, taking the Cap standard with them and locking it in from early on. I'm sure their routes just kept getting longer as the proto-NCR started to spread and the caravans needed to seek untapped markets. There were also settler/refugee groups like the Khans and the remnants of the Master's Army/CoC as well as missionary/exploratory groups like The Followers, who likely brought the idea of cap currency with them when they set out into the areas beyond the core (which were largely tribal and possibly lacking the concept of a universal standard of exchange). Vegas is about 1/5 of the distance from The Hub that Klamath or The Den are, as the crow flies, and even closer than that to Shady Sands, and most of the major settlements in the region lie on major highways. They probably would have fallen into the core region's mercantile sphere of influence long before they were reached by its military/political one.
As to the Legion, Caesar may ban the possession or use of certain items, but beyond that he generally leaves economies intact and even takes pains to protect trade. It's worth noting that he, himself, comes from an area that trades in caps and he may even have spread the idea to a few tribes during his work with the Followers, so he recognizes how ubiquitous their use is in the west. He'd likely mandate a phased universal transition to Legion coin once he'd defeated the NCR and consolidated his empire in the north and west, but until then, much of the extra-imperial trade his territories are going to be engaging in is going to be with regions that use other forms of currency, and it's not going to do his economy any good to bar their use.
