I remember when the video came out, there were excited talks-in-passing at work with some of the older co-workers, who had been former Smiths fans during their youth, asking like "oh, did you see Morrissey holding a guitar in the Pretenders cover?", and it seemed that this was the first time they have seen or listened to him since the 80s. So, I think this song helped to bring Morrissey back to the attention of folks who had almost stopped listening to music in the late 80s, before they focused on the family and job thing instead. It rekindled their interest.
For me this song is one of my three "good companion songs" I listen to when a stretch of supposedly "good times" ends and the same old shit starts again, making you wonder if there can ever be a meaning in life. I have the 7" single here and the cover looks nice, even though I am not very keen on 7". I prefer the older tradition of 12" singles. I like Morrissey's manly approach to the song.