The source you cited is likely wrong.
Preferred stock would have custom, ad hoc terms regardless. A company could definitely sell preferred stocks with detachable warrants that still gets dividends.
Maybe the author of that article is implying it's standard practice to do such a thing, but I don't think so. The value of the preferred stock would be little without detaching the warrant and selling it. No one would keep the warrant unless they effectively wanted a call option instead of the preferred stock. By definition, 'detachable' implies they are two separate securities that do not depend on each other. But even with non-detachable, the two securities together are effectively a call option instead of preferred stock. Basically, in that sort of structure, the warrant detracts from the value of the preferred stock instead of being 'upside', which it's designed to be while lowering interest/yield for the company.