There is a problem with hoarding tabs and multiple windows of a browser. If you have a window with 100 open tabs, and then a second window with 3 open tabs, and then you close the 100-tab window first and 3-tab window second, then browser will silently close all 100 and save only 3 tabs you have closed the last.
It is easy issue to avoid until that one time you accidentally forget about it. So I try to avoid multiple windows of Firefox.
Also if we are talking about a separate icon on the taskbar, then why not make it a dedicated app with proper settings, notifications and stuff, which you can't forget or disable?
You can convert the tab into a window and keep it visible :)