Why isn't Sivir a midlaner? Her kit is made up of abilities from midlaners...
Q-Ahri's Q, Orb of Deception
W-Katarina's Q, Bouncing Blades
E-Morgana's E, Black Shield
R-Master Yi's R, Highlander
Her kit is built upon other abilities from midlaners, so why isn't she mid?
Firstly, Master Yi isn't exactly considered a viable midlaner but that's fine.
The abilities you listed from other midlaners aren't necessarily what makes them good midlaners in the first place. For example, Morgana's black shield, while useful in mid lane, she's nothing without the rest of her kit and the combination of everything makes her viable. Katarina's Q sets her up for all her other abilities, it's not just the Q on its own.
Coming to Sivir herself, she's a late game ADC because of a number of factors.
1. Her Q while it has been buffed and does good base dmg, it's not up often enough as one of her only abilities for damage in an actual all-in fight vs the enemy midlaner. Her Q is also easily predicted and/or dodged, whereas someone like Ahri has her charm to ensure that both parts of her Q hit.
2. Her W scales very well off of AD and applies crit multipliers (late game scaling) as well as having a built-in auto attack reset which again implies ADC because more auto attacks scale with more crit and all the items take time to farm and need to be done with the safety of a support.
3. Other than her E shield, she has no escape pre 6 to ganks and you're more susceptible to ganks in the mid lane, more of a reason why she is better suited to the ADC role over mid. She needs the protection of a support. Post 6, she has her R for increased mobility but unless you know you're getting ganked or you manage to dodge a skill shot because of it, it's no real escape.
4. Finally, back to her W again, it adds nothing in a 1v1 other than an auto attack reset and only adds potential poke from bounces off of creeps in the mid lane overall. In bot lane, she actually has 2 targets and the bounce is worth something. She also wouldn't be fulfilling any different role to the ADC in the game, leaving your team potentially without an assassin or consistent ap damage from a mage, while also having a harder time in lane compared to others.
Hope this helps somewhat and that I've answered your question. I don't do this regularly.
Top it off with her Q weakening with every minion hit but early game she'll struggle to not be pushed out of lane.
generally the reason why adcs are not played in mid lane except for the exception of corki/lucian/. They lack waveclear/burst and have a hard time winning the lane on their own and their power spike takes longer then most mids.
Nothing is stopping you from playing Sivir mid so she can be a mid laner if you played her there but you will most likely have a lot of issues vs good players.
Here is a list of some problems Sivir mid would have.
1. Scales up slowly compared to other mid laners (Most mid laners spike at 1 item however sivir doesn't have the greatest 1 item spike so she will have a hard time early-mid game in the solo lane)
2. Mana/waveclear issues (as you mentioned in your post her spells would actually suit mid lane pretty well. However the huge issue is they are not spammable if she uses her W+Q to waveclear she will go oom and have to either back and lose xp or get poked/bursted out of lane cause she has nothing.)
3. Roaming issues (common mid laners will most likely be able to match sivirs push early because her low dmg she will not be able to instantly push a wave in until mid-game so it would be really hard for her to be impactful on the map with her ult, additionally it will be harder to use her ult in mid lane because its a shorter lane.)
4. easily poked/bursted out of lane.( She can easily be poked out/bursted by Orianna and Syndra in lane it would be really hard for her to trade back evenly early.)
Those are some of the main issues with sivir mid.
I hope this helped :)