If a SID has a low level restriction, perhaps anything less than 3000ft, we should be engaging the autopilot to better manage the level off.
I agree with a lot of what you said, but strongly disagree with this. Perhaps it's because my humble RJ doesn't climb as fast as your 777 (presumed from your username), but I think that a level off (even below 3000ft) hardly constitutes a high workload environment.
If I find myself screaming up at 4000fpm on a low altitude level off, adjusting the power setting does the trick most of the time.