Q: iOS 9/iTunes 12.3 not syncing app through devices

Ok I think I figured it out. Go into the Itunes store, and make sure you're logged in. (Click on account.) After that, go back to the home page and click on Purchases. It should have all of your apps there. Click the download all button, and boom! Worked for me, hope it does for you! My iPhone was plugged in.

Yes you can re-download previously purchased apps but this does not help with the management of bandwidth. Downloading again just uses up scarce bandwidth. For some that may not be a problem but with bandwidth constraints it is a problem.

The simple solution would be:

iTunes —> (Account) menu —> Purchased —>  Apps —> All —> (iPhone or iPad) —> then download all apps you’d like to appear at Apps Sync tab at your phone window of iTunes.

But as SantafeNM says, we've always been able to re-download apps to our computers, I don't believe that was a problem for anyone on this thread.

I have always been able to download to my computer and synch across to any of my Apple devices.  I do not use iCloud.  I also keep all of my iTunes content on my computer and back it up regularly.

In the past I was also able to download direct to device when an update showed, and then when I synched that device the updated app transferred to my computer into iTunes and updated my stored app so I could then synch it to my other devices.  This was at a time when I had a limited broadband account so helped keep my broadband usage down and avoid additional costs each month.

Now you cannot synch an app update from a device to your computer.  You either update direct to each device or update to computer and synch to device.

I don't have a particularly fast broadband connection, although it is now unlimited (and I notice even the limited service my provider used to have has now changed to unlimited which resulted in the charge for my own account dropping to the amount they used to charge those who had a limited allowance - good result).  I still prefer to have everything backed up to computer (and external hard drive back up) and I do have a 2 TB hard drive on this PC so plenty of capacity. 

From what has been said previously on this thread Apple intended us to no longer be able to synch apps from device to computer, but they still let us synch from computer to device.  So yes, if your device will not update apps then you would need to follow the path of re-downloading apps from your purchased option to computer and then synch across, that has not changed and is as it has always been.

The issue here is the two way sync its not working any longer before on iTunes you could update an app on your iPhone or iPad  and then sync your device on iTunes and the app will also be update on your iTunes library on you mac this feature was handy for people who own a lot of devices and there bandwidth is limited now you have to update every device individually or first update the app on iTunes and then sync your devices on iTunes.