Cacti are succulents, but succulents are not necessarily cacti. Aloe are succulents, but not cacti. Allow me to do a bit of quote sniping:

Aloe isn't very potent at all, it's just very mildly toxic (when ingested) succulent tissue. You'd have to eat an entire plant to feel sick from the toxins, and you'd already be sick from the leafy taste long before you'd finished eating the plant anyway.

That's not how it works. When beauty products, food, medicine, etc, contain 'extracts' of something, that doesn't mean that they took the thing in its entirety, took a little bit of it and put it in the product, what it means is that they took only the 'good stuff' and got rid of everything else, and then mixed a little bit of that good stuff into the product. As such, there is no 'dilution' in the sense that you speak of, but 'extraction'. To give an example, if a yoghurt contains 'carotene extract' to give it an orange colour, it doesn't mean they blended a bunch of carrots and pumpkins and put some chunks in the yoghurt, they simply extracted the carotene responsible for the orange colour and got rid of the carrots and pumpkins (which, without the carotene, aren't orange). Once extracted, the link with what it was extracted from is really only used for marketing purposes (or anti-marketing purposes). By the way, a failure to understand this, the interplay between general biology, chemistry, physics and genetics, is one of the main reasons why people are afraid of GMOs.

It doesn't, in fact one of the use cases for applying Aloe vera to the skin is to lessen the pain of (sun)burns. It would be quite counterproductive if it did exactly the opposite.

Regardless, there is no real scientific evidence that Aloe has any beneficial effects at all, whether applied to the skin or ingested. The drinks they make with chunks of Aloe in them taste pretty good, though.

This is not to say that there are no plants with medicinal or otherwise beneficial properties. For example, Chelidonium majus is really potent in dealing with warts. Instead of going to the doctor's to freeze them, you can simply apply a few dabs of the plant's sap on a wart and it'll kill the wart dead. Depending on which continent you live on, you probably know it as "that plant with the orange sap that stains everything". Extracts from the plant are also used in medicine to treat cancer and HIV.