Unless dead stuff is sticking up and being distracting to me, I don't worry about it. Stuff that's sticking up, I trim off and let it fall between plants to become part of the 'mulch,' or put into compost if it's too big. Very few plants look different if they were 'cleaned up' vs. if they weren't, once the growing season gets going.
If you're pressed for time, don't feel like you need to clean up a flower bed. It's one of those busy-work things that supposedly "needs" to be done according to some, and intimidates people in regard to both spending time and feeling they don't know how to do it when they're reading about gardening, that's not really necessary. Most micro-manage garden chores are in that category.