It's more nuanced than that but you could do a lot worse than that list. Fat profile matters, and smoke point matters, e.g. olive oil is great but if you're frying stuff with it you're turning a lot of it toxic; avocado oil is better for high heat.
The reason for olive oil not being used for deep frying is mostly taste and cost, as far as I know.
https://www.masterclass.com/articles/cooking-oils-and-smoke-...
Found the video: https://youtu.be/l_aFHrzSBrM
Do you have a source on that? What is toxic about it? Really curious, because I cook a lot with olive oil.
note that the experiments were carried out without food being cooked. While cooking, the water and steam which comes from the food being cooked aids the process of hydrolysis. The absence of food in these trials may have allowed for a greater impact of oil oxi- dation when compared with other deterioration reactions
They didn't test the affects of water and food contact on stability and note the potential significance of hydrolysis.
But just going by that, I'd avoid all refined oils and heating/frying.
Also what’s the best substitute for vegetable oil for baking?