You're looking at it the wrong way
Let's take an average working joe. They can log in once when they arrive at work, once at lunch and say once before they leave for home.
Old
Time: 09:00
Start: 100 Energy
Schedule: 4 hours (52 Energy)
End: 4 hours ~ 64 Energy & 4 Productivity
Time: 13:00
Start: 64 Energy
Schedule: 4 hours (12 Energy)
End: 4 hours ~ 24 Energy & 8 Productivity
Time: 17:00
Start: 24 Energy
Schedule: 2 hours + sleep (0 Energy)
Final: 10 hours ~ 100 Energy & 10 Productivity
New (Hotel)
Time: 09:00
Start: 100 Energy
Schedule: 2 hours + 2 hours 5 star sleep (52 Energy)
End: 4 hours ~ 83 Energy & 4 Productivity
Time: 13:00
Start: 83 Energy
Schedule: 2 hours + 2 hours 5 star sleep (35 Energy)
End: 4 hours ~ 66 Energy & 8 Productivity
Time: 17:00
Start: 66 Energy
Schedule: 2 hours + sleep (26 Energy)
Final: 10 hours ~ 100 Energy & 12 Productivity
New (Barracks)
Time: 09:00
Start: 100 Energy
Schedule: 2 hours + 2 hours 6 star sleep (52 Energy)
End: 4 hours ~ 88 Energy & 4 Productivity
Time: 13:00
Start: 88 Energy
Schedule: 3 hours + 1 hour idle
End: 4 hours ~ 28 Energy & 10 Productivity
Time: 17:00
Start: 28 Energy
Schedule: 1 hours + sleep (4 Energy)
Final: 9 hours ~ 100 Energy & 12 Productivity
More productivity, same time frame.