Basically, these are the 4 professions I don’t have on any character yet.
Now, if I make 2 more alts, does it make sense to have Engineering + Jewelcrafting for one, and Inscription + Enchanting for the other?
I have plenty of character who have gathering professions, 2 with Mining and 2 with Herbalism so I can certainly supply the mats. Is there any reason why this would be a bad idea, or shall I go on with it?
Your plan makes sense as Engineering and Jewelcrafting both use ores, so having them on same character is practical. For the two other professions, combining Enchanting with Inscription also works fine even without having any synergy between them.