@baguette Oh my, it's been several years since the term "leaky gut" was a catchall diagnosis for all kinds of ills. Please take a look at this article, especially the myths surrounding identifying the condition:
https://pmc.ncbi.nlm.nih.gov/articles/PMC11345991/
The puzzles of food sensitivities is complicated, your friend's proposed elimination diet would follow what the pro's recommend and probably give you better answers than the proposed blood tests.

Here is one caveat: No cheating or it doesn't work!

Take a look at this recent discussion of several alternatives, their benefits and drawbacks:
https://pmc.ncbi.nlm.nih.gov/articles/PMC6682924/
Wrap yourself in patience - without immediate allergic or gastric reactions, this type of experimentation can take time and often several tries to find the answers for your body.

I can tell you that I am intolerant of wheat (not gluten) and after about 15 years without eating it, I have a very satisfying diet with a lot of great bread/dessert products that don't rely on it. Yes, sometimes I look twice at delicious holiday breads, but the pain is not worth the momentary pleasure.