That is incoherent. What are you talking about? This is completely untrue and doesn't even make sense:
"When considering the price of assets, a generalized rise in prices has the same relative effect as inflation in consumer goods; the decline in the purchasing power of money relative to other assets."
Someone owned the asset before you bought it and that person became wealthier as the asset prices rose.
If I buy a house for $250,000 and suddenly it is $500,000 then I am suddenly $250,000 wealthier. If I buy 2 liters of milk for $6 and a week later I want to buy more but now it is $12 then I am poorer because the things I consume cost more.
Economists use the term "inflation" to refer to the loss of value that some consumables suffer as the money supply grows. But the concept doesn't apply to assets because the owner of an asset can sell the asset and reap the rewards. By contrast, if I buy some milk, and keep it in my refrigerator for 20 years, I can't then sell it and benefit from inflation.
When we talk about economics, inflation refers to a loss of value. Rising asset prices refer to a gain in value.
Under your crazy definition, where inflation applies to assets, there has been no gain in wealth since the beginning of time, since the rising prices of all assets are thought of as a loss instead of a gain, under your definition.
About this:
"than restricting their use to a single "dictionary of economics" definition pointing to a single metric with predefined inputs"
Every profession uses certain words in specialized ways. If you don't like the way some topics are discussed in a given branch of knowledge, then just don't participate in those conversations. I will assume, since you are on Hacker News, that you don't have a problem when engineers give special meaning to "message" or "bus" or "event" or "queue" or "broker".