A term or phrase expressing the cheapening of a quality by measuring it in monetary terms

In current usage you could call this

"a crass monetization of <bravery|effort|...>"

In recent colloquial usage "monetize" has moved from its technical meaning of "to convert to currency" to also mean "to make money from something" or an attempt to do so. The term itself, even without a pejorative adjective, has a slightly negative connotation as it often occurs in the context of "monetizing debt", a euphemism for a sovereign printing money to reduce national debt.

It's not a single word, but putting a price on something is the behavior you describe.

Could you use : "Commodification"?

It is the transformation of goods, ideas, or other entities that may not normally be regarded as goods into a commodity. Incidentally, as a commodity, they have a price.

In the Marxist theory, this is perceived as something quite negative.

Google shows eight entries for the neologism mammonification, which occasionally is used to mean commercialization of things that ought not be commercialized. The root of the word is of course Mammon, referring to "The desire for wealth personified as an evil spirit" or to "Wealth, material avarice, profit".

The verb cheapen has, among its several senses, one of bringing down the value of something by bargaining for it. Aside from sexual senses, verb prostitute has senses "To use one's talents in return for money or fame" and "To make another person, or organisation, prostitute themselves"; a sense similar to those is used in wiktionary's example sentence, "Yet again a commercial firm had prostituted a traditional song by setting an advertizing jingle to its tune." Verb whore has some similar senses.