There's a lot of reasons to organize spell hotkey assignments that were considered.
One is familiarity, as you mentioned, making sure that buttons sit on champions of similar playstyles. For example, many champions have their line skillshot on Q, so we wanted Q to be his "line" spells. Some champions use W for shields, others use E for shields, so there wasn't a clear winner for that one other than enchanters preferring shields on E compared to mages.
That leads to the next consideration, which is mechanical feel. Generally you want to spam Q the most out of all of your abilities, so that was another reason to put his low cooldown damage spells on Q. It feels a little awkward to constantly spam Q + W or W + Q, so his wave clear and poke spells were put on Q and E so you can double tap or dance between them using your point and ring finger. Your middle finger is then used less frequently and with more intention, preventing too many "fat finger" inputs due to spamming two buttons next to each other. This also let the spells with more setup time live on W, namely QW and EW, so you had time to recover your hand position after awkward combos.
Next is shape consistency. QQ is a line cast, WQ is a line cast, and EQ is a line cast. QW is an area circle, WW is an area circle, and EW is an area circle. We tried to do the same for the QE, WE and EE spells but found the constraint too much to make useful and interesting spells and chose to let that be the wildcard slot. Shape consistency helps to ensure your last press in a spell sequence is predictable in targeting so you don't get confused on how position yourself due to a weird swap.
Then we have spam presses, namely QQ/WW/EE. We wanted QQ and EE to be the best generic spells for new players learning how to play Hwei, and both generally need to be used proactively to capitalize off enemy mistakes. Conversely, WW was chosen not just for the circle area shape but also to make reactive shielding a fast button press so you don't lose time when trying to block damage.
Finally, we have combo flows. WE -> EE -> QQ is a frequent combo to deal a ton of damage at mid range and because of the button layout prevents most bad inputs (W to start, spam E, then spam Q). Another example here is WQ -> QE -> EQ/EW for disengage which has each last button be the next button. We also have EW -> QW that has your fingers dance between the sides and centers.