Disclaimer. I am silver, this is my opinions. If you disagree make an argument, and actual argument. Not rank calling.
Good things about Shyvana's design:
1: There is no ability on Shyvana that it feels bad to level. A lot of champions suffer from this "Damn... I am forced to put a point in hawk shot." Thing. With Shyvana, people can argue the value of every single ability choice. Her E is a bit iffy for maxing second but it still doesn't feel bad leveling it.
2: All of her active abilities feel impactful and fun to use. Her E isn't just on hit %HP magic damage, it is a skillshot ability that does initial damage as well. This makes it more interactive and fun, it makes you feel like you are doing something. It isn't just a passive that provides a buff, you actively cause the buff. Her Q feels great every time it hits, I just love this ability, regardless of build, it makes any on hit effects or AD feel amazing, it is both good for chunking and DPS. Her W is great, movement speed and AoE damage feels fun and good, but more than that, it rewards actually hitting with melee attacks by providing flat, on hit magic damage. Lastly, her ultimate! Oh my goodness is this amazing. I can leap through the air, turn into a dragon, get AoE on my E and Q, get a minor singed trail on my W, plus I get a huge buff to defensive stats, a free increase of 10/15/20 armor and MR. Feels good.
3: She isn't that hard to balance. She requires tuning here and there, and any buffs/nerfs to on hit and AS items do affect her. But as her kit doesn't have a million random active effects and complex mechanics, it is easy to keep her at a medium balance by tuning numbers. She has shined at times(devourer) and hurt at times. But overall there isn't the hate fest that people have towards Riot over champions like Azir, where he is useless when nerfed in some levels of play, overpowered in other levels of play when buffed.
4: Quick farm junglers can be fun and interactive. It's just less about ganking, and more about securing early dragons, counter jungler the enemy, stealing camps, and using your superior dueling power to counter gank better ganking junglers.
5: Hybrid damage. We have so few hybrid damage champions left, but my goodness does it feel good. Sure, it means you cannot itemize heavily into penetration, but it also makes you hard to itemize against, meaning you can invest in damage and tanking items instead. Shyvana is also fairly versatile in her builds due to this.
6: Medium item flexibility. Shyvana has good item flexibility. Not too much like some champions who can build anything but succeed, but she also isn't a one trick pony of one item. She can viably build any of the following stats: Attack Speed, Movement Speed, AD, Magic pen, On hit effects, HP, Armor, MR, utility, active mitigation, lifesteal, critical strike chance and HP regen. AP, Armor pen and Crit damage are more questionable on her but usable. Only Mana is truly useless on her. Unlike the bruisers who build Black Cleaver, Deadmans, Spirit Visage and the other same 3 items every single game, her build can vary, even her jungle item. Warrior for CDR, early game dueling power and scaling on W? Bloodrazor because Attack Speed and On hit are so good for her? Cinderhulk for survivability when you are behind or against heavy burst teams without HP stackers? Runic echoes isn't the best option but... it's possible. Overall, flexible champion, but not too flexible.
7: Dragon, rawr.
Bad things about Shyvana as a champion:
1: Her buggy, wonky hit box ultimate, which has a hard to read mechanic, people have been complaining about since her release. Also the lack of unstoppable status during her ult(which people like Vi, Sion and Hecarim get) just feels awful. Jumping through the air as a massive dragon only to be stopped by the first pebble thrown your way is just... ugh... it destroys her post 6 ganking potential against anybody with mild CC and it feels just bad during team fights.
2: Her passive is not very interactive. This is questionable. Her passive use to be on her ultimate. The CDR on her Q, the extended duration of her W and the on hit damage of her E use to be on her passive and instead her passive was on her ult. But the new system puts the passive for her abilities on the abilities, and made the MR and Armor from her ult her passive, letting her benefit from it from lvl1. I can argue both sides. She needs it to retain her early game strength and already has a lot of passive power, so just adding it to her base stats and giving her a new passive could be bad. But also it isn't interactive other than being doubled during Dragon's Descent so it isn't 'fun' to use. But it overall is a good, solid design, so changing it just to add another 3 hit passive, shield or other popular Riot passive, might not be a good idea either.
3: She is heavily item reliant. While she can itemize a lot of choices, she is far too affected by any changes to her stat sticks. As seen when devourer was removed, she lost a lot of power. The reason? Because she is an AA based champion with an AA reset double hit. I don't know how to fix this, but it is an issue she suffers from.
4: She lacks any pre-6 ganking power. Yes, she CAN gank with red buff and chilling smite or Exhaust. And she can counter jungle. And she can counter gank well. But if for any reason the enemy team organizes against her counter jungling, wards well, or the enemy jungler 'counters' her counter jungling. She has a bit of a lost purpose until late game. This could be good or bad, but it should be looked into, just to see where she could use some changes.
5: Her W has too much power and her E and Q too little early game. Making lvling W first the only option.
6: She can no longer be played top. She is one of those few junglers who can literally only be played in one role.
7: She has a low skill ceiling. This isn't necessarily bad, she still saw LCS play in 2012-2015. And there are plenty of high level players who play her. And after all, people could argue many champions have a low skill ceiling like Udyr or Nasus, and say that makes them bad in high levels. Trick2G would say otherwise. These champions, like Shyvana are about map control not mechanical outplays. But all the same, to encourage more people to invest in playing these champions and building skill, map control and strategy with them. I think we could work to find some way to give her a higher skill cap and more map interactivity, without of course destroying her base playstyle and fantasy.
Shyvana is a solid and fun champion. And any rework on her would have to be VERY careful to keep the core things people love about her; high dueling power, quick jungle clear, high map control, very in your face punchy gameplay, dragon, split pushing and hybrid damage. Maybe even keep in her ability to sort-of build AP. The last thing we need is a Mord/Skarner style rework, that changes her identity and base playstyle. Still, the champion could use some work, and some quality of life changes(especially to her ultimate), in order to keep her valid, and a fun investment for current players.
Thank you for reading.