When the start menu gets long and even more when it overflows it is nice to have folders for eg. games, office apps, image apps etc.
The main reason I like the start menu is that I sometimes forget the name of applications I use seldomly and I forget what apps I have installed.
Edit: One thing I forgot to whine about is the configuration panel. In the old one you had everything in front of you instanly. The new one is a joke and I never seem to remember which feutures you need can change in the "mobile friendly" blue one, or the kinda a folder one.
When I want to do something, I hit the launcher key-combination of whatever OS I'm in (the Win/Super key in Win8/10 or GNOME; ⌘Space in macOS) and then type the first few characters of the name of what I want. If I know the search database is up-to-date (i.e. I haven't just installed the program, I then just immediately hit Enter before the dialog even shows results.) The program opens.
I feel like a Start Menu makes a lot of sense... for people for whom using a mouse is somehow a lot easier than using a keyboard. People who can move their fingers easily but whose wrists+forearms are immobile, for example. Or people operating the GUI through a thin-client app on a candybar-style cellphone. Or people using Windows on their TV with one of those Wiimote-like "air mouse" pointing devices, where switching to the keyboard has the friction of flipping the thing over, taking away your ability to move the mouse while you type. Or, for that matter, people using a game controller, ala Steam's Big Picture mode.
But in the regular case, where you have a keyboard and mouse in front of you, and are in a relaxed default position with one hand on one and one on the other? I can't see the benefit—for just launching programs.
-----
Now, for discovering programs... I'd never know about the "accessory" programs that came with an installation if I couldn't browse. I still recall the first time I installed Sim City 2000 and realized it came with a separate program called SCURK (a level+resource editor for the game.)
But it's been a long time since I've installed a program that came with accessory programs that way. These days—probably because of the influence of app-stores—every feature you get from an installation of "an app" is always accessed through the main binary of the app. And if it can't be, then they just don't bother to distribute it. (See also: macOS and the paucity of uninstallers for programs that install LaunchDaemons. You usually have to google for a script!)