The goal of a systematic review, with or without meta-analysis, is to cover as many studies as possible that fit your pre-planned objectives, eligibility criteria and quality assessment strategies for doing the review in the first place. You should aim that your output closely reflects the reality or phenomenon of interest, and one way of doing so (although this not always successful) is to ensure that you have at least considered all previous studies (which is easier said than done as some studies that tackle your research question may not have been published) - think of it as analogous to the law of large numbers, where sample size refers to the number of studies.
A systematic review that, in one way or another, disregards eligible studies for seemingly unjustifiable reasons (such as not including either extremely old or latest studies even if they fit your protocol's inclusion criteria) should automatically cause suspicion from both reviewers and readers. Another issue altogether is dealing with the inherent differences between older and newer papers on the same topic (e.g., in terms of diagnostic criteria, assessment tools, and intervention quality used that may have gradually changed through time). Remember that systematic reviews and meta-analyses are more than just pooling combine-able data in forest plots; discussing the similarities and differences between studies that would provide the backdrop for your results and conclusions is important as well.