Why would mind flayers let you keep anything? You're a prisoner. You should have been stripped of everything but your clothes.
At the moment of "harvesting" - yes, people become their prisoners. It would make perfect sense to strip them of everything valuable or dangerous. However, after being infected, we are no longer their prisoners - we become their agents. Lae'zel's remark about Us makes it perfectly clear.
So, logically, we should all start without any equipment. Not sure how we are going to defeat the first group of imps then? With bare hands and harsh language? A good solution to this was used in BG2, when you could pillage a chest in the nearest room, with plenty of mundane equipment to fit any class. However, in BG2 you've got your entire party right in the first room (except for Yoshimo, but he came relatively well-equipped). That's not the case here, with Shadowheart coming rather late to the party.
They could have placed a chest with SH's equipment relatively close to her pod. For example, in that room behind her, where we pick the key from the corpse. But that will require special dialogue lines, so that Shadowheart would be able to tell us to go searching for her stuff - with Lae'zel naturally objecting. Or maybe make it part of the cinematic of her release, when she rummages through some stuff, finds her armour and equips it, all being done without any interaction from player. Or, even better, Lae'zel would give her her armour, saying that she found it while looking for her own. Since we "don't have access" to their inventories now, that probably would be the best application of deus ex machina principle, without making the whole scene too much of a cringe.
It looks to me that Larian has chosen the easiest way to get around it, by leaving characters' equipment with them. This, of course, created other discrepancies, which seems to be always the case with the "add more homebrew to fix issues with homebrew" approach. Oh well, we have what we have.
