Do you need one horizontal cable manager under each patch panel/switch/server?

I'm re-doing a rack for a small office with two non-profits.

We have several 24-port 1U patch panels, but I'm consolidating it into 48-port 1U patch panels (Monoprice).

I've also bought several of these cable management bars (fs.com) .

This is what I'm planning:

https://i.imgur.com/9NXi6Db.png

My question:

1. Do I need one horizontal cable manager under each patch panel?
2. Do I also need one horizontal cable manager under each switch or server?
3. Is there a neater way of doing the above?