Research into the areas you mention has led to a movement to rename "the tragedy of the commons" to "the tragedy of open access" (one that I personally agree with). A key figure in this research is Elinor Ostrom, the first woman to win a Nobel Prize in Economics, for her and her husband's Vincent's empirical and theoretical work on how people in small communities can manage shared natural resources. Her 1990 book Governing the Commons: The Evolution of Institutions for Collective Action, was incredibly influential. But she was not the first to work in this area, other figures include Deidre McCloskey (then Donald), who was publishing on the role and agriculture of English commons in the 1970s, and arguing for the commons' efficiencies in terms of managing risk, and James Acheson, who in the 1970s and 1980s started publishing on the development of property rights in lobsteries in Maine, and the management of common property resources. 

Drawing on Ostrom's work (she in turn drew from many others' work as well as her own field studies), the success of communal ownership of land/resources in classical/medieval Europe and other areas depends on particular principles, such as clear boundaries around who can access the resource, a system for monitoring members' behaviour, and that the rule-making rights of the community members are respected by outside authorities. Ostrom was well aware of the cases of environmental exploitation under conditions of open access, such as massive overfishing of the oceans and deforestration (page 2/36, Basurto & Ostrom, 2009). 

So this is "communal ownership" in the sense still of limitations on who can use the resources, and limitations in what ways members can use them, rather than "communal ownership" in the sense of open access. To quote from Frischmann et al's 2019 retrospective article in the Journal of Economic Perspectives: 

Open access implies no ownership or property rights. No individual or institution has the right to exclude others from the resource. Hence, all who want access can get access, typically for free. By comparison, commons involve some form of communal ownership (community property rights, public property rights, joint ownership rights). As a consequence, access to the resource is restricted to the members of the relevant community, under more or less restrictive conditions, and nonmembers can be excluded. [Emphasis in original]

So coming back to your original question, modern economic historians recognise communal ownership as a way of efficiently managing resources and avoiding environmental degradation. But this is not to say that all communal ownership regimes invariably lead to efficient outcomes: the details matter. Bailey , in a discussion of common rights in medieval England, for example says:

Regions characterized by strong social structures – dominant and/or high-status lordship, large manorial holdings, a high proportion of customary tenants, a unified community – were likely to possess relatively formal and regular field systems, whereas closed or irregular systems with few communal regulations were usually found in regions possessing a weak social structure. (page 165).

Given the importance of social factors, and the complexity of ecologies, your specific question of whether lands/resources were poorly managed is hard to answer, let alone relate this back to any particular form of ownership. Lower output of some resources may be the result of mismanagement of the resource, or it may be the result of other social stresses (e.g. a civil war being fought over the land), or it may be the result of outside changes, such as changes in market prices or climate. I think though we can say with some confidence that peasants throughout history have done rather better at managing resources efficiently than academics and policymakers used to think, and that any outsider studying how the locals manage resources should be starting from a point of humility.

Sources (not linked in text)

Bailey, Mark, 2010, Beyond the Midland field system. The determinants of common rights over the arable in medieval England, Agricultural History Review, https://www.academia.edu/download/32658662/Beyond_Midland_Fields_AGHR_58.pdf

Xavier Basurto, Elinor Ostrom, 2009 Beyond the Tragedy of the Commons,  Economia delle fonti di energia e dell'ambiente, https://dukespace.lib.duke.edu/dspace/bitstream/handle/10161/6504/Basurto%20and%20Ostrom%202009a%20EFEA%20Beyond%20the.pdf?sequence=1

Brett M. Frischmann, Alain Marciano, and Giovanni Battista Ramello, 2019, Retrospectives: Tragedy of the Commons after 50 Years, Journal of Economic Perspectives—Volume 33, Number 4—Fall 2019—Pages 211–228, https://www.aeaweb.org/articles?id=10.1257/jep.33.4.211

Cox, M., G. Arnold, and S. Villamayor Tomás. 2010. A review of design principles for community-based natural resource management. Ecology and Society 15(4): 38. [online] URL: http://www.ecologyandsociety.org/vol15/iss4/art38/