Yep. Shyvana needs that as well as more things. Shyvana is in a really bad spot and seems like riot doesn't give a fk.
There is no much more to say that people have not said yet about her...
Shyvana without her ult is legit a worst Udyr. If you die lategame, after your respawn you will be basically useless while all other champs will have their ult again. A good way to solve this would be, as you proposed, have her Ultimate recharge while she is dead. Shyvana passively generate 1-1.5-2 fury per second. Early and mid game she really didnt need to generate that too while dead. However, lategame is a must so in my opinion she should generate the same that now while alive but while dead she should generate something like 0-1-2.
Also she needs her q nerfs be reverted as well as much other things...