I do the same, but depending on the song, I try to get the swing from the snare, hats and toms, and strive to get the kick on the beat to give the lock. Bass and kick drum especially need to play as one, beat wise. That doesn't mean the odd double hit, or twiddly bits on the bass, but the bass and drums are the engine room for rhythm, and then everything can swing around it, but with the thing locked. I was doing a track yesterday that was quite loose - and it was a bit of a mess in places. I'm a rotten drummer and often play ahead of the beat (I call that style, my friend who is a drummer calls it rubbish playing) quantising the kick drum only sorted it out.
To Gecko - I've been doing videos for years and have to admit I really struggle with story to songs. I discovered recently in a forum topic that I simply don't hear lyrics. People were talking about songs I know well and talking about the story. I had to go back and re-listen and they were dead right. So many really interesting stories I'd missed for maybe 50 years! For me, songs with a melody and words are just a melody. I've thought about the words I sang on stage every show. I didn't know the meaning of any of them.
I messed up one song because I started to listen to the words I was singing, and realised there was a story - and was so surprised I forgot what was coming next!
After all these years, now I have ideas for videos I'd not had before. I suspect my video would have been very similar to dame's - a sequence of shots cut nicely together.