In 4th Edition, encounters could take a long time, but in 5th Edition, encounters should be fast enough so you can have 20 or more good fights in a single session.
Wow. This has not been my experience at all.
Combat is way faster than 4th edition but how long are your sessions that you expect to go through 20 good fights? My group averages more-or-less 1 fight per hour; slightly more if the fights are all lined up ready to go, slightly less if they spend a lot of time exploring or talking or deciding which way to go next.
Slowing the XP rate or introducing level-grinding (which sounds phenomenally boring to me) may backfire if fights start taking longer than you expect.