Definitely a yes from me. The way I play the game is that I typically start with a created character, then I play them for a while and after accomplishing various things I like to have them start a family. Something that has become sort of a tradition for me is that I like to play as the first born for every family, which typically means that I move them out usually after becoming a young adult. Most of the time I would like to take things with me, but of course as it is the only way that happens without mods is if it fits in their personal inventory or if I simply give them the money to buy any objects I want them to have once they're in their new place.
I don't know if it has been updated recently or not, because unfortunately the mod creator died a few years ago (RIP Scumbumbo), but there is also a mod called Packing Crates. I remember using it on PC, and it allows you to take objects that normally go into the family inventory and place them in a container that goes into the personal inventory. The way it works is that you get the crate in build mode, and then in live mode you simply enable the packing option on the crate then objects should have a "pack in crate" option when you click on them. Once you have everything you want you disable packing mode, put the crate in your sim's inventory, then you can unpack everything on the new lot.
If nothing else EA should at least implement a feature similar to that mod. I doubt EA knows or cares who Scumbumbo was, but it would be really cool to see a packing object (possibly other objects as well) in the game that references them in some way especially since they really seemed to have a lot of passion for Sims 4 and modding it.