Pressing first letter of user account name does not select user in login window

Solution 1:

Did Apple remove this feature for some reason?

No, this has not been removed. You should still be able to select users at the login window via the first letter of their user name, or via using the tab and arrow keys.

If not, is there a setting anywhere to switch this feature back on?

At the outset let me say this may not be the likely solution for you. However, I have seen this behaviour and thought it was worth mentioning in case it helps you or others.

If your Mac running El Capitan is a desktop Mac (i.e. iMac, Mac Mini, Mac Pro, etc) and it happens to be plugged into a UPS (i.e. an Uninterruptible Power Supply), then shut down your Mac and unplug it from the UPS. Now plug it into another AC power outlet and reboot it. Check to see how your login window behaves now?

If on the off chance this is your situation and your Mac now works as you'd like, an option that may help you is upgrading your OS to macOS Sierra. I say this only because macOS Sierra offers some native support for using a UPS and this may or may not rectify this issue.