It's been a long time, at least in Las Vegas terms, since we last addressed this issue (8/4/05, so almost three years, in fact) and not surprisingly the landscape's changed somewhat since then.
As we commented in the original answer to this question, in the early days when hotels were smaller and more intimate, it was common for rooms to have balconies looking out onto the Strip or inward to the pool area, as the Stardust did and the Tropicana continues to (about two thirds of the Garden Rooms have balconies, but they're located in the low-rise buildings and overlook the garden pool area, not the Strip). Today, it's much rarer to find a room with outdoor access for a number of reasons, some of which may be obvious and some less so.
For one thing, Nevada has one of the highest suicide rates in the nation and jumping (be it from the Stratosphere Tower, the Hoover Dam, rooftop parking lots, overpasses, or hotel balconies) is a popular choice. Hence, most hotels don't even have opening windows, let alone balconies. Similarly, but on a less macabre note, with the prolonged extreme summer heat and the cold winters, it's difficult and expensive enough for hotels to regulate ambient temperatures in a controlled environment, let alone if half your guests are leaving their windows/patio doors open.
Bugs are another issue. In the springtime, when the weather's at its most inviting and sitting outside on your balcony to watch the lights come up on the Strip might seem like a pleasant early evening activity, you run the risk of admitting some unwanted visitors into your room. About a year ago we received a query from a guest staying at Planet Hollywood who'd wanted to open the window vents in his room so he could hear the Bellagio fountain show, only to find a sticker requesting him not to: "Moth season -- please keep vent closed."
Building balconies obviously adds to the construction costs of a hotel plus, in a city that really would prefer to have its guests playing down on the casino floor, or at least catching a show or enjoying some kind of fine dining experience, it's well known that the policy has always been to make the standard hotel rooms functional but not so comfortable that you'd want to hang out in them too much. (Hence, not such a surprise that the non-gaming off-Strip Platinum hotel on E. Flamingo does offer private balconies, as does the Hard Rock, which pretty much just wants you to party wherever you are.)
It's no big surprise, therefore, that when it comes to rooms with balconies, the options on the Las Vegas Strip are somewhat limited, particularly at the lower end of the scale.