Go ahead and fix it to your taste. I don't have anything against the concept of cladistics, but the current practice violates a principle that it took a lot of painful experience to absorb. Namely, if the practitioners of an art can't/won't speak in clear, simple language, that's usually a symptom of massive confusion on their part. I do think the subject deserves an entry. DJK
I've seen some cladistics and as far as I can tell it uses no more jargon then any other field. A lot of the terms, as stated, are used by other methodologists as well. But more to the point, except for perhaps clade each of the words expresses a concept which doesn't really have a compact synonym in normal English. So they're somewhat unavoidable, just like jargon like endoplasmic reticulum is unavoidable in protistology.
Aside from that, the article above seems fine, except perhaps for a negative image cast towards the subject. But whether that's deserved or not I can't say; I am not a biologist, so have no idea about the objections you present. As stated, most trees I've seen come out relatively close to earlier ones - and when they don't there are darn good reasons - and most recent sources on evolution I've seen are fairly pro-cladistics. But I really don't know that much.
Ah, one more thing I noticed. Cladistics is not a classification system, as stated on [Linnaean Taxonomy/Talk]?. It's a methodology for elucidating evolutionary relationships. Taxonomy has, for a long time, intended to reflect these (which also, btw, makes the point about continually changing classifications moot - it's a problem we already have), although cladistics people tend to make an insane amount of subclasses, infraclasses, subinfraclasses and so forth as they go through.