We checked this on the bench. When an R2008SB receiver is used with an SBD-1 and analog servos the servos act exactly as you mention, but if we put in digital servos everything works correctly.
When an R7008SB receiver is used with an SBD-1 and analog servos everything works correctly.
The higher frame rate of the R2008SB w/SBD-1 vs. the R7008SB w/SBD-1 is the reason.
R2008SB w/SBD-1 – 6.7ms frame rate
R7008SB w/SBD-1 – 15ms frame rate