My objection to this class of stylistic advices is that they use tricky arguments to prove their point. Usually the authors choose an extraordinarily ugly piece of text (or even make it up, as is probably the case with the description of bicycles in your link) that abounds in the word or grammatical category they despise and want to argue against, then reformulate it in normal language, taking care to avoid the undesired thing, then pretend having proven a general rule that the despised part of language never should be used, save of course few exceptions which they rarely bother explicitly describing. The readers see two pieces of text, one ugly and one readable, and usually accept that the ugliness is caused by the expression they are advised to purge from their writing (which is even not always the case) and that the less they use it, the better (which doesn't follow).

Good writing is not achieved by avoiding everyday expressions and regularly used grammatical features. There are things to be avoided in writing or speech, for sure. But if you are going to ban the most frequent verb which also plays the role of copula and is part of passive and progressive constructions, you are constraining the expressive power of the language, limiting the effectivity of communication, and even making your writing harder to read. It has as much sense as saying you should never use the prepositions "in" and "on"; certainly you can rewrite any text so that the rule is satisfied - and since you are forced to search for alternatives interesting and novel expressions may appear as a by-product - but ultimately, because of artificial limits you have put on yourself, you are not free to say exactly what you want to say.