How to attack saves varies greatly depending on specific fantasy leagues, unlike other scoring categories. In leagues that value closers highly, the top tiers are likely to be pushed up into the early rounds of drafts thanks to a clear trend: More relievers are recording saves while fewer are individually reaching 20+. Again, your league may vary, but Edwin Díaz and Emmanuel Clase have become common second/third-round fantasy picks in early 2023 drafts.
Roughly counting, only about half the league enters the season with a named closer, with the other half being a complete guessing game (and you can be sure there will be chaos among those currently holding down the job).