Why doesn't China just assassinate Tsai and be done with it?
This would be a very stupid move that would only do Beijing's cause more harm than good.
Despite of what the English vegetable is, in the eyes of Beijing, she's actually much more preferable to the "Vice President" of Taiwan, who is even more vocal and pro-independence that the English Vegetable ever is.
Assassinating Tsai would only serve to rile up and galvanize Taiwanese support even further for declaring formal independence from China when Lai takes over the "presidency" of Taiwan. This ultimately breaks the status quo of which China is working so hard to preserve.
Moreover, if China really did such stupid thing, rest assured that the US-led West would jack up their propaganda machines to the eleventh, aiming the bullseye towards China and loudly broadcasting "Look at China, China assassinated Taiwan's president! China is the threat to world peace and stability! Beware if you do anything that goes against Beijing's wishes, China will come for you too!" to the world. It also becomes much easier for the US-led West to find justification in supporting Taiwan's independence (and war with China under the guise of "defending democracy and freedom").
What else can China do to defend her action in this case? There is none. And the rest of the globe would scoff at China resorting to such dirty and immoral tactics, which leads to severely damaging China's image on the world stage.
None of these would even remotely work in favor of China, and nobody in Beijing is even remotely stupid to believe that would work.
Furthermore, neither Russia wanting the Ukrainian President killed, nor Israel wanting the Supreme Leader of Iran killed. Because having them dead is only going to make present situations so much worse.
So why bother with Taiwan's "president" at all?