For example, "Get a free widget with this 12 month magazine subscription ($12.99/month)!" And then people will genuinely argue that the widget is "free" in spite of it being tied to $150+ in mandatory expenditure.
The word people are looking for is included, the widget is INCLUDED with a 12 month/$12.99/month subscription, there's nothing "free" about it.
Nothing about the above is contrived either, these "free" ads and claims are all around us.
For example a harddisk with a terabyte capacity does not have space for 2^30=1,099,511,627,776 bytes but about 10% less. Some disk management tools however were based on base 2 measurements, and the customer might cry foul because the tool reported only about 930 gigabytes, err gibibytes.
For example, suppose somebody says "I'm so hungry, I could literally eat an elephant." It's obvious that they're being hyperbolic because of course nobody eats elephants. Adding literally just adds to the hyperbole because it makes the sentence that much more ridiculous.
It's a figure of speech and perfectly legitimate, IMHO.
Seems silly to use a word in a sense opposite what it literally means for emphasis. But whatever you enjoy.
A linguistic prescriptivist might say it was wrong because people might say something they want to emphasise like 'my phone is literally blowing up' - but according to the traditional meaning of the word literally, that means it would be literally blowing up, like an actual explosion.
Once 'literally' just means 'emphasise this' then you have to go into further contortions if you actually want to express something that means something that is exactly as described, not figuratively.
I suppose emphasis can turn into exaggeration, then literally is indeed a bad fit. But it can be emphasizing something without exaggeration too.
I.e. "literally days ago". Which indeed can mean a few days ago, but it's emphasizing it. I don't think it's a wrong usage.