Don’t think those are super comparable.
West Wing is still very much part of the older style long-running network shows where the aim was to make a load to into syndication. It’s obvs not an obvious procedural show like ER or a NYPD Blue, but it still has an issue of the week that is resolved in a single episode, so each episode can be watched essentially independently, with the longer arcs being less important.
The Wire is more from the post Sopranos / HBO time, the auteur / golden age of TV period where the focus is on telling a whole story over the length of a season or more, where there’s far more focus on subplots and characterisation, and the whole thing is slower and more impenetrable if you don’t watch the whole thing in order.