Is it poor style to use adverbs ending in "ly" in formal writing?

I came across this infographic which contains the following claim:

Some grammarians consider "ly" ending adverbs as bad style in formal writing.

Are there any serious style advice sources that actually make this dubious claim? What's the theory for how avoiding such adverbs improves writing?

I've done some further research and found that this notion is widespread, but there is little citation or authority. Where did this idea come from?

For what it's worth, here's a blog entry that claims "Aspiring science-fiction authors receive one piece of advice above all others: Forsake the adverb, the killer of prose. It's terribly, awfully, horrendously important." — Seriously, What’s So Bad About Adverbs?

To make the point about as clear as I can - using "ly" ending adverbs is BAD WRITING for fiction writers. — Those "ly" Ending Adverbs

Solution 1:

Some cooks hate garlic. That doesn't mean garlic is bad. That in order doesn't mean eating raw garlic before a job interview is a good idea.

The rule of thumb is "do not make up adverbs".

Do use adverbs if they concisely convey a specific quality, better than a more expressive verb would. I asseverate most people prefer an adverb - simple verb pair than an overly fancy and obscure verb containing given quality.

Avoid them when they cheaply replace a descriptive expression or a verb that pinpoints given quality.

Do not use them at all if you avoidantly try to replace whole sentences with them, or redundantly repeat the sense of the verb they describe. You are able to make up adverbs impunitively, or abuse obscurely occurring ones, or arbitrarily give them new meanings, but don't do it. It's bad.

Solution 2:

Some grammarians consider "ly" ending adverbs as bad style in formal writing.

Grammarians, when discussing style, could certainly suggest what they feel is good. That doesn't set a new rule of grammar.

The -ly adverbs have a purpose of their own and when used carefully, serve well in both general and formal writing.

[Essentially a comment] Beyond this, the question is exclusively in the domain of writing style, not language. (Similar style applied in any other language might have similar implications.)

Solution 3:

Seriously, I defy anyone to tell me that using adverbs that end in =ly is really an element of poor style. Anyone who does is undoubtedly a pedant.

Generally speaking, there is a certain school of thought which asserts that verbs and nouns are strong, adjectives are weak, and adverbs weaker still. These are the same people who hold that the passive voice should be avoided, and so on. While there is a germ of truth in some of this, writing that cleaves to one set of prepackaged strictures tends to become boring and predictable.

Solution 4:

-ly does define an adverb, after all.

But, looking at your source matter, I think, from the perspective of selling one's work, that the admonishment has most to do with prospective readers: multi-layered descriptiveness, even when accurate, could tend to tax the attention capability of too many of them. ...in line with neo-modern trends in writing and reading...and even thinking (or, as was more accurately stated, feeling).

Perhaps it would be best desribed as a case of inverted literary license: standards you may feel free not to follow to make your point in writing. Or perhaps it"s just a way to keep editors employed?