I have three suggestions to circumvent three major annoyances with hosting games. But I don't know if any of those are actually possible.
1. When on you are hosting a game and go on the desktop a notification sound rings and or the FAF or FA icon blinks when someone joins your game.
2. A feature that allows you to send a wake up sound to somebody who might be on the desktop through the FA ingame lobby. Like in TS.
3. Bring back the after game chat tab but differently. The chat tab will open as soon as you JOIN a game. It will automatically close 5 mins after either the game is over. If you leave the game lobby before the game even started it will only stay open for 1 minute. It will stay open until 5 mins after the game is over if you left before the game was over. This will make rehosts and such way more easy to pull of.
These are three things that I think would make hosting games way more pleasant.
Please spare me the "stop suggestion stuff - just do it!" nonsense. Not everyone who has a suggestion also has the skills to make it happen.