Before iOS 9, iOS apps could be backed up to Macs and PCs via iTunes1:
"If you try to transfer purchases from an iOS 9 device in iTunes, you may notice that apps won’t transfer to your hard drive. Similarly, when backing up an iOS 9 device in iTunes, the 'Backup Apps' dialog will simply not appear. App data will be backed up, of course, just not the application themselves."
Adding insult to injury, iTunes 12.7 removed the App Store, closing the door on downloading/backing up iOS apps from there:
"If you own a Mac or even a Windows PC, you will no longer be able to download iOS apps to your desktop to sync to an iPhone, iPad, or iPod Touch."
You may want to back up an app before it disappears from the App Store or preserve an older, better version, e.g.,
MiniKeePass - final version only added an EOL nag on every launch
Insight Timer - mutated from a simple meditation timer to a social media saturnalia
Milebug - perennial mileage-tracking favorite pulled by developer, despite it continuing to work as originally designed (i.e., completely offline) even in later iOS versions (tested in iOS 13 & 14)
iOS apps can still be downloaded via iTunes 12.6.3 (does not run on Mojave or higher), Apple Configurator 2 (with some caveats), or iMazing:
To back up all apps on your iOS device to apps/ in the current directory of your Mac, jailbreak your device, install usbmuxd, start iproxy, then:
$ scp -P 4444 -r root@localhost:/var/containers/Bundle/Application apps/
$ mkdir Payload
$ cp -R appname.app Payload/
$ zip -r appname.ipa Payload/
iTunes 12: click iOS device icon → drag appname.ipa under "On My Device" section
Apple Configurator 2: double click iOS device icon → drag appname.ipa onto "Apps"2
Xcode 11: Windows → "Devices & Simulators" → click iOS device icon → drag appname.ipa into box under "INSTALLED APPS"
iMazing 2: click iOS device icon → Apps → Copy to Device → browse to recovered appname.ipa → "Select"
Apple Configurator 2 also allows installing an iOS .app via Actions → Add → Apps... → Choose from my Mac...
/mac | Sep 28, 2020