Can I really "wear" my luggage?

Yes you can. Anything on your person does not count as luggage allowance. Earlier this year I had to fly on some airlines where carry-on had a very low weight limit and on some flights which did not allow a personal item in addition to a carry-on, so I designed a vest and had it custom made for exactly this purpose. What inspired me was this video about another photographer needing to go through check-in with a good amount of gear.

In reality, carry-on are almost never weighed, so I just went in as normal. When I did get weighed, that was only two times (in my whole life even!), I simply moved extra contents from my carry-on and the personal item into my vest. Right at the check-in counter and they said nothing. In one case I emptied my entire personal item, plus stuff from the carry-on and put one into the other since I there was no allowance for a personal item.

Both times I did that at check-in and there were no issues. The vest was designed to handle 12kg with pockets large enough to accommodate a laptop, two professional cameras and four lenses, plus lots of additional items, papers, books, etc. When worn, this gets quite uncomfortable which is why I went each time wearing it but mostly empty.

If you scroll down to point 4 of this page on moneysavingexpert.com then you can see how the journalist Martin Lewis wore his luggage while flying.

It looks like this is still allowed.