Word for suggesting solutions to a problem solely to demonstrate contempt for the expected problem-solver

Solution 1:

"Smartass" is the best I can come up with (both adj. and verb), and it fits quite well I'd say. I don't know if there is a word that exists that's more specific to your scenario though.

Solution 2:

A couple of adjective options:

Vindictive -- Having or showing a strong or unreasoning desire for revenge.

Spiteful -- Showing or caused by malice.

Both of these convey the idea that the proposed "solution" isn't so much about fixing the problem, as getting back at someone out of sheer vengefulness.

Solution 3:

Perhaps their suggestions are sarcastic, snide, or facetious?

Solution 4:

Straw man arguments work somewhat in the way you described. It has the "negative" feel that you're looking for. These arguments are meant to mock the opponent. This is a bit more general than your hypothetical with X, Y, and Z.

However, your other example, "There should be a law that slow people lose their driver's license for life.", sounds like a rant and not like a straw man argument.