Is comma needed here?
- "inexpensive, but effective, resources"
Can comma splices be used instead of "that" and "and" here?
- It is clear, X destroys homes, businesses.
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A comma is used to create a pause. Commas are needed in other specific instances such as lists. The phrase "inexpensive, but effective, resources" works without the commas and with the commas. The pause in the middle of the sentence may be more annoying to readers, however.
The phrase "It is clear, X destroys homes, businesses." is not grammatically correct. The comma should not be used to replace insignificant words. It is only done in headlines and even then it is used exclusively for newspaper headlines and the like. (Headlines are more art then writing: see the link below.)
In the first sentence, no commas are necessarily needed, because "but effective" is not a nonessential clause/phrase that doesn't have a coordinating/subordinating conjunction, a lengthy phrase or dependent clause, or an introductory clause or phrase. However, it improves clarity and emphasis to put commas surrounding "but effective" to separate contrasting coordinate elements and/or to indicate a pause. The Purdue University suggests that these types of phrases are placed at the end of the sentence, perhaps because to avoid too much interrupting pauses in sentences:
The resources are inexpensive, but effective.
See number 7 on Purdue University English Comma Usage for more details. It is not a firm rule, however, so it is okay to place "but effective" in the middle of sentence; just don't overuse it in a paragraph or essay, as in not having it appear twice in the same paragraph to avoid over-pausing.
Also, like Edwin suggested in a comment, em dashes instead of commas may be an option. Using em dashes "--" are useful for setting off parenthetical clauses/phrases that completely interrupt a sentence. However, they are best used to in place of parentheses, rather than commas because they "break" off the sentence (like how dashes are used to signal dialogue being cut off), so I wouldn't recommend them in your sentence.
In the second sentence, it would be technically incorrect grammar, yes. It is, though, perfectly fine to use in poems and informal writing for the purpose of emphasis and addition of drama. I have also seen these comma splices used in titles of Internet articles, and I suppose it would be fine for physical newspapers and articles as well (though I don't have any experience with those). It should not be used for non-poetic formal writing like informational essays, research papers, and such, where grammar is considered. One note is that "is clear, X destroys" indicates an omission of "that" so it would seem grammatically correct but since the omission of "that" almost always results in no comma in between, it would still be considered a comma splice.