When you reach a new town in a new part of the world, you need to go to the weapon and armor stores in order to upgrade all of your equipment. It is a simple routine, and it has been part of almost every RPG I have ever played, going all the way back to Dragon Quest. This need to upgrade equipment at every new town occasionally gets altered, made more complicated, or even completely subverted, but far more often it is not. At its most basic, every character will get a new weapon and new armor at every town, and the growth in power of those items will scale perfectly in proportion with every other character's new weapons and armor. While this is perhaps the most common model for how characters upgrade equipment across the course of the game, it usually detracts from a game more than it helps.
In a situation where new, more powerful equipment becomes incrementally available as the player progresses through the game, the cost of this equipment will inevitably become little more than a tax the player has to pay. In such a structure, the game designer must design the game under the assumption that the player will always have the best equipment available. This means that a player who, for some reason or another, doesn't have the latest equipment will be at a disadvantage and have a more difficult time with the game. At the same time, acquiring the new equipment doesn't give the player any kind of new advantage (since the enemies will have equivalent increases in power to match) or new kind of strategic option (for this post, I am assuming that equipment only grants the usual bonuses to attack and defense, and new equipment only gives bigger bonuses), so acquiring new equipment only maintains the status quo. As such, the cost of the equipment is little more than the minimum amount of money (or whatever) that the player needs to pay in order to avoid a penalty and keep things the same as they were previously. In many cases, the need to pay off this "tax" can simply be a source of frustration and stress for the player (this has happened to me countless times), and may result in the player feeling required to spend a lot of time on boring activities (AKA money-farming/grinding) in order to progress.
If new equipment is little more than a tax to be paid in order to avoid a penalty, then it would be better off it that entire aspect of the game were removed entirely. After all, I have never actually missed the act of buying equipment in games that didn't feature it (Xenosaga Ep. II comes to mind). More importantly, it seems like it would be easier for the designers if there was no equipment, since it means they don't need to guarantee that there is enough money (or whatever) available for the player to pay the "equipment tax", it would mean that there would be fewer variables in character balancing, etc. If equipment is simply going to be improved incrementally, then there is no advantage to having it that would justify adding all that complexity. If there is some aspect of an equipment system that justifies its existence, it is usually only limited by an incremental upgrade system (for example, a rare and difficult-to-acquire weapon being completely replaced by a weapon found in an ordinary shop later in the game).
There are many games I can think of in which equipment adds a lot to the game experience, but none of these games have the stereotypical "buy new equipment for every character at every town" system. The Fire Emblem scheme, where weapons will eventually break and most of your equipment for the entire game is comprised of simple iron and steel weapons, makes equipment management an extremely important part of strategy and makes unusual weapons extremely important and memorable. In SaGa Frontier, pretty much all the equipment you will ever see is available to be bought from the start, but cash is so limited that you need one of the game's several infinite money tricks in order to ever buy anything, making the items you acquire through luck and exploration extremely important. In Final Fantasy III, inequality in the availability of viable equipment can be annoying, but at the same time it forces the player to adapt by trying out new classes and strategies. Both the Suikoden and the Super Robot Taisen games combine non-transferable equipment upgrades with very large teams of characters, so it is impossible to upgrade everyone, forcing the player to make tough decisions. There are many ways to make equipment work, but just buying a new, mathematically-superior weapon at every town is not the way to do it.