I dislike shuffling my people around also, but I can understand why they capped the population growth of planets per week. If you take over a planet from an enemy and all your current planets are full, it's unrealistic to expect 5-20+ billion people to just suddenly flood it to max in a week or two. If you conquered the planet you can always think of it as a slow process in which you integrate POWs into your society and that the planet is already nearly full.
Maybe it is as fast as your government can process survivors and immigrants into being proper citizens. As they mention in the updates, the tax paying population growth isn't just babies being born, it is supposed to account for immigration and emigration which is why your population drops at low approval (they aren't dying off, they are leaving or not paying taxes). Similarly if you kill a farm, I wouldn't say that the people die that week, they are probably just ticked at you and not going to pay any taxes or up and leave for another planet. Persons on your transports are already citizens so they can integrate instantly.
One thing I don't understand is why there is a soft cap on low quality planets that can be circumvented by manually transporting people there, after which, they don't leave or die as long as you have enough food.
1) launch transport with some % capacity.
2) land transport on a full planet
3) *zoooooooooom auto-focus on the other side of the galaxy*
4) find your way back to the planet you left the transport on
5) repeat steps 1-4 until xx billion capacity transport is full or you want to smash your monitor
6) land full transport to low population world
7) see step 3
8) find your way back and repeat the process as necessary
I wish auto-focus would die. Killing that alone would make this process much less painful.