Why can’t lanthanum through lutetium and actinium through lawrencium all be in group 3?
Since I am neither clairvoyant nor able to travel back and forth in time, I can only guess what IUPAC was thinking.  But there is no guessing that the inner transition elements do not completely fit in with Group 3 chemically.
One major chemical difference is in the oxidation states the elements may achieve, and thus the stoichiometry of compounds with nonmetaks that have strong ionic character.  Whereas the Group 3 elements overwhelmingly form compounds in the +3 oxidation state, other oxidation states are more likely for at least some inner transition elements.  While in some other groups there is more variance linked oxidation states, this is little seen in Group 3 whereas, below, variance in oxidation states is more common with inner transition metals.  Especially note the higher oxidation states in the examples that follow, which would not be expected in a group generally defined by elements normally having only three valence electrons.
Among lanthanides, cerium achieves a +4 oxidation state commonly enough to be called &quot;ceric&quot; and be available as a reagent for redox reactions, as in ceric ammonium nitrate and cerium(IV) sulfate.  Cerium can also form +4 as well as +3 ion cores in the metal by either including or excluding its $4f$ electron in the metallic band structure, leading to a transition between two FCC phases [1].  At the opposite end, europium accesses the +2 oxidation state much more readily than a true Group 3 element, leaving half-filled valence shell, and thus overlaps the heavier alkaline earth metals in its chemical properties.  Wikipedia reports that

In anaerobic, and particularly geothermal conditions, the divalent form is sufficiently stable that it tends to be incorporated into minerals of calcium and the other alkaline earths.

With actinides, oxidation states departing from the +3 predominance of Group 3 are more common.  Well-known examples include thorium forming a highly refractory oxide in the +4 oxidation state and uranium achieving oxidation states as high as +6 when combined with fluorine.
Reference
1.
Johansson, B., Luo, W., Li, S. et al. Cerium; Crystal Structure and Position in The Periodic Table. Sci Rep 4, 6398 (2014). https://doi.org/10.1038/srep06398