Price change is not fundamental to economics. It is fundamental to a post-Fed inflationary policy that seeks for a low (or at least a consistent) unemployment rate. That being said I think this is a great case study of "menu costs" on steriods.
Kudos for pointing out that this is a classic example of menu costs, but price changes occur for many reasons besides the Fed. Even if you had a fixed supply of gold coins and nobody could ever mine new coins, the value of those coins would change in proportion to the value of the overall economy, and that will tend to change for all sorts of reasons such as population growth.
But there isn't a fixed amount of gold. More gold gets mined when the demand for currency rises relative to the price of energy. The price of oil roughly tracks the price of gold not because gold is a magical denominator, but because an ounce of gold represents a certain amount of sunk energy that mined it.
Au contraire - price change is a fundamental aspect of economics. Why would a new competitor selling the same commodity ever expect to be successful? Because they've figured out how to provide the same product for less expense. So even ignoring expected price decreases due to technological progress, we'd still expect to see prices occasionally decreasing due to organizational progress.
Not to contradict, but to add detail: land, labor, capital, material resources and market seldom exist in the same location for any specific good/service, and the cost of distance (and the cost to overcome those distances) affects market bearable prices. It need not be technological progress that makes one competitive, it may just simply be favorable proximity to resources and markets that gives you an edge.
Coca-Cola (the syrup) is produced IIRC in only one place, and bottled/canned with local waters in regional centers because the cost of shipping a product that is mostly water around the country/world will drive costs up.
Many auto-makers in the US became "competitive" by closing factories where labor costs were high and opening them where they were lower. Many foreign producers of cars opened factories in the US to offset the increases of labor costs in their own countries while also decreasing shipping costs (especially for Asian car makers who cannot as easily ship to the Eastern US) and nullifying punitive tariffs.
The way/speed/reason/etc for a change in a price is certainly one of the most fundamental topics to economics. For one, it's a topic that grabs the mind share of both macroeconomists and microeconomists, and there aren't many of those!