I figured the regeneration from Ten to Eleven was so violent because he held it back to visit the previous companions.
I don't buy the "held back" explanation. There's a far more plausible one. What "killed" the Tenth Doctor was the same thing that "killed" the Third in "Planet of the Spiders" -- a radiation overdose. And after the Third Doctor's lethal exposure to radiation, he was lost in the time vortex for weeks before finding his way back to UNIT HQ and finally succumbing. Which is consistent with how radiation poisoning works in reality -- its effects are delayed, and a lethal dose can take days or weeks to kill. So there's no reason to expect that the Doctor would
have regenerated right away after lethal exposure to radiation. A delayed reaction is exactly what should
happen. So there's no need to assume he held anything back.