The reasons historians tend to concentrate their efforts in a narrow era is because they know what it takes to develop historical expertise in a topic, and convey the best truth of the past currently available. They know what the primary sources are for a given era/topic, and more importantly, how to interpret them. They know the important secondary works in their era. They know what key issues are considered settled and which ones are up for debate; they understand how the different sides in the debate affect our understanding of the era. They are interested in the past for it's own sake.
Tuchman brings none of these things. She reads sources at face value that really do not mean what they say (there's a lot of fictional examples that she takes as Gospel Truth), uses n=1 to draw sweeping conclusions, tries to make a 14th century to mirror post-WW1 anxieties (the "distant mirror" of the title), and isn't much interested in anything that doesn't fit her preconceived narrative. She sure writes in different eras, and as a straightforward prose writer she's amazing, but she doesn't bring a historian's expertise to her work. At all.
Some historians absolutely do work cross-context, and very well. My favorite example is of course Paul Freedman, who started off as a groundbreaking, award-winning medievalist and now does U.S. food history so well he was asked to help compile the AHA's Companion to Food History. But this takes A LOT of time and energy, resetting your dial from Expert to Amateur and rebuilding.
Funnily enough, the historians best positioned to have expertise in multiple contexts are PhD students passing through comprehensive exams. In a traditional US PhD program with comps/quals, you complete a massive reading list in 3-5 different contexts, generally focused on a topic within them (like "late medieval social history", "African Atlantic history"--so, you know the key secondary works, the important debates, and the ins and outs of working with some of the most important secondary source types for the field.
And then the dissertation makes you squander that breadth for depth, and it's just easier to keep plowing forward after that in a relatively straight line.
In addition to the case of Paul Freedman, given by u/sunagainstgold, we might also note the especially dramatic example of Sir Ian Kershaw, the globally-renowned historian of Nazi Germany, who began his career as a medievalist specialising in the study of 13th-14th century priory accounts from Yorkshire, and who was prompted to radically shift track by a 1972 German research trip that resulted in an encounter with
an ageing Nazi who remarked that 'if you English had come in with us, we'd have destroyed Bolshevism' and that 'the Jew is a louse'.
It's safe to say that Kershaw's switch in focus was rare and surprising in the early 1970s and would be a lot harder to pull off today.
In short: No. Barbara Tuchman is a bit of an interesting case because she was never professionally trained as a historian, but as a journalist. Although a lack of professional training may make it harder to get work, it also allows flexibility between disciplines (especially if you're established as a more freelance writer without restriction). Most professional historians work in pretty narrow fields. For example, a historian of modern France will generally do work between 1750 to the present and even then will deal with a common set of issues (although this can vary).
For example, one historian I know (Laura Frader) has worked on topics ranging from labor history in provincial France to the formation of the welfare state and European integration between the 1870s and 1970s, but she focuses on gender as the subject of her analysis in all of these works. Others may work more closely on specific topics like the rise of the far right, the age of world wars, or agricultural history, but most are quite narrow in focus. Interests tend to shift as a career goes on, but they generally stay in the same field unless they do outside training (say in other methods or disciplines).