There are two ways to consider this question. The first, which seems to be the intended aim, involves whether specialists in other disciplines should be involved in writing the history of those disciplines. One of my hats is the history of science and technology in colonial Africa, so that requires that I become familiar with the bodies of knowledge I discuss. The major issue in that instance is that often the knowledge I am talking about was long since banished from the active curriculum for training new scientists or technicians. This means that, while I interact with specialists in those fields, only those specialists with an interest in the history themselves are open to really extensive engagement.

My personal example involves mapping, which has changed dramatically from the age of optical survey, rough plane-tabling, and physical compilation relative to today's practices. There is, however, no shortage of geographers who have some interest in the past methods and critical meanings of their subject, so we do have common foci. Our work, however, tends to bend in different directions: mine is more involved with society, culture, and the effects of that knowledge, while they spend much more time with technical matters and issues internal to the practices of the field. We do, at least, speak the same basic language--and as with languages, it's important to be conversant (and to converse!) if you are to study something.

The second question, which is implicit, involves disciplinarity itself. The division between a lot of disciplines as separate units is an artifact of the turn of the 20th century (or earlier), and arose from a European model of how one divided subjects and fields. That baggage of that particular nationalist moment is still with us, and most scholars are aware of the artificiality of the lines. However, if you study in certain areas that emerged after the early 20th century (such as African history) there's a tremendous amount of cross-disciplinary discussion and has been for a long time. We have borrowed very freely from linguistics, folklore, anthropology, literature, music, art, political science, medicine/public health, and so forth; for more specialized subjects, we've also been attuned to the same critical discussions going on in other fields (such as geography, for my case). That's also true for other disciplines crossing into history; I have colleagues in Anthropology who are doing amazing, deep sociocultural and spatial histories of the western Sudan, and who could easily be in our department instead. This erasure of boundaries is also increasingly visible in more established fields of history, especially as we've moved away from overarching narratives in favor of a more expansive consideration of history (e.g., "US history" now has many, many thematic and regional subfields with different methodological toolkits).

My short answer to your question is "yes, there should be more cooperation and collaboration," but I would leaven it by saying that there is already a great deal of connection and crossing-over--perhaps more than most students of history realize!

The short answer is yes, there does need to be some collaboration, and indeed, that happens quite regularly. Economic historians do talk to, work with, and read the work of economists. Historians of science do have a familiarity with the science and frequently do talk to scientists (though, as /u/khosikulu notes, that usefulness may decline as one goes backwards in time — talking to a physicist today about Boyle's theory of the vacuum is likely less valuable than it might seem, since they don't see the world the way Boyle did, and concluding "Boyle was wrong according to the present day" is not a good way of understanding Boyle). Diplomatic historians do overlap heavily with people who study international relations in the present day (and vice versa). Historians of mathematics frequently do engage with mathematicians. There are tons of overlaps — the idea that historians just hang out in their own disciplines in an Ivory Tower fashion is not true today, and may never have been true.

Obviously there are greater and lesser collaborations, of course. Some historians of science really do want their work to be read by scientists. Most do not, and so the extent of communication is going to necessarily be mostly one-directional. Separately there are issues of authority: scientists approach history differently than historians do, and they often resent that historians of science do not defer to present-day scientists for judgments relating to science. (See the famous "Science Wars" incident of the 1990s.)

Should there be more cooperation, or is the amount of cooperation right now fine? Depends on who you ask, I suppose. But any historian worth their salt is capable of recognizing when they are wading into the expertise of another field, and capable of dipping a toe into that other expertise (even if that just means calling up someone who is an expert and talking with them — I have a plasma physicist I call up whenever I have questions about nuclear fusion, I do not pretend to fully grok the ins and outs of the science). I am not sure on what basis one would argue there should be more or less of it — I know of no great scandals at the moment regarding historians being particular out to lunch on any other field's expertise, but that isn't sufficient to declare something being "just right." But each historian acts as an individual entity, and this is a very broad issue, so making a collective judgment like that strikes me as being pretty difficult.

That's been one of the benefits of being in such a small field (art marketing, phenomenology, and authentication). I can't stick with my own kind because it doesn't exist beyond me, so I have to go spelunking myriad fields, and I've worked with with people in medical imaging, musical instrument repair, chemists, police, curators, psychologists, economists, filmmakers, auctioneers, art historians, critical theorists, theologians... whereas other people I've worked with are in much more insular research environments.