To see why it's not worded that way in the Wikipedia article, imagine each sentence in the article implicitly preceded by "According to source x,..." -- source x of course being the relevant citation. If the cited source states that he "said", then using "claims" or "allegedly" does not accurately reflect the degree of certainty expressed in the cited source. Veracity of that source notwithstanding.
It's fairly common to word things that way in Wikipedia articles, though of course not for every citation. It's a judgment call whether it should be or not, since adding a qualifier in-text more strongly contextualizes the claim as being from the source, rather than in "Wikipedia's voice".
For example, I recently wrote an article about an ancient Roman politician. A number of sentences are in the form "[Scholar A] argues that the person did X [cite]" rather than "The person did X [cite]". I'll use the second form for uncontroversial facts, but the first form when it's more like a proposal from a particular scholar which isn't necessarily an accepted consensus viewpoint.
