Talking politically and practically, the obvious difficulty that she would have going into the next election, let alone as Prime Minister, is that she is a loose cannon. She does not think before she talks and is absolutely happy to offend anyone and everyone. When she does, she retorts with the whole "I'm just telling the truth" line, which of course is not only wrong but misses the point. Politics is about messages and how you deliver them, and the delivery is often just as, if not more important than the message. Farage is a prime example of someone whose messages are usually pretty awful when you scratch the surface of them, but he repeatedly finds very effective ways of delivering them. Johnson, too, had nothing more than a paper thin plan on Brexit, but his delivery of that message was excellent going into the 2019 election.
Badenoch has no real message at the moment, but then she's been in post for all of five minutes, so she has time to develop one. The problem is that even if she does develop one, there is nothing that she's shown which suggests that she'll be effective at delivering it. Basically, she's really not shown that she's got any sort of ability as a politician specifically. So yes, as PM she would really struggle, and would likely be pretty disastrous even with a decent majority. The big concern for the Tories, though, should be how someone like Badenoch is going to both make inroads into Labour and fight off Reform at the next election. They're in a really precarious position, as are Labour given the their seat majority is not nearly as stable as it looks. The political landscape in this country could change significantly at the next general election, and at this point I'm almost expecting it to.