The review process must become more transparent. The reviewers and their assessment of the work must become public when the paper is accepted and published. This in itself will prevent some nefarious citation-begging.
In addition, some guidelines could be mandated concerning citations to be added or removed. For example, for each reference you want the author to include, you must explain why it should be included. Not just "this has been done before" but "the work you describe is similar to the work done on p.4 of [new ref.] but differs in X,Y and Z and is still novel because of invention/method A,B,C. Therefore, you build on their work and should cite them."
To the others in this thread: remember that peer review is often an iterative process and the authors and reviewers have multiple rounds of review in which the authors can choose not to implement some suggested changes, such as adding citations. This is often a small debate. The editor of the journal has the final say and can overrule the decisions of the reviewers (publish / reject) if there are good grounds to so.
Also a small note: the reviewers are selected by the journal editors based on expertise. That means, especially for smaller fields, that many prominent papers are written by the reviewers simply because they are the experts. It is easy to conclude that this leads to bad behavior but it is often the case that there simply are no other papers available with such specific details. Of course, this is not an excuse for malicious actors which are also rampant.