The lack of diversity has several roots. One of them is the networks. Networks often include people from highly ranked institutions (universities) of developed countries. Even people based there but in other institutions might suffer from the same problem. I would say that this is the main issue. In my discipline, it is almost impossible to publish in the top 5 because of this issue: one needs to have presented the paper at seminars in top places earlier.
These days, in the areas where preprints are common, refereeing is just single blind (as one can just google the title).
Kehinde M. Adeleke to add to José-Ignacio Antón , one of the most difficult issues author face when writing for journals is discrimination. Whether it is simply an error of omission or driven by design, the "arms-race" over increasing impact-factors and rankings makes it difficult for new voices to find opportunities. Additional, the costs of publishing--driving even the wealthiest libraries to cut their subscriptions--means people may not know where they should publish. This really connects to the question of networks, authors writing who are isolated and/or limited in their ability to engage with others may not know where to go. One important solution that some journals are doing is to open the editorial process, and invite and involve new voices to participate as reviewers and editors. This is a way to establish connections and support the networks we all need to do good work. It is also critical for journals to reach out and ask people to write. Do so is an important way to bring new voices into dialogue and establish connections that will support collaboration and make everyone better. This is such an important question and issues--thanks for bringing it up!
Apart from the fundamental questions raised above (to which we could add indecent article publishing charges), there is also the more down-to-earth issues of language editing and manuscript formatting. Most researchers from low-income countries do not speak English as a first language and lack resources to pay for their manuscripts to be edited for language and format (i.e., to respect the instructions for authors). Because the peer-review process is conducted on a voluntary basis by researchers who could do something else of their time, they are much less patient with manuscripts suffering from language or formatting issues, regardless of their scientific value. Some journals offer the "your manuscript, your way" option (for formatting), but this does not solve the problem of reviewers not liking to receive oddly formatted manuscripts. Language is a more profound issue (you cannot get your message across if readers struggle to understand it), and there is urgent need for affordable (even free) language editing services. Billionaire editors could dig into their pockets to offer such a service, but they don't, or they charge too much.