What are the fundamental issues that make LOX as a regenerative coolant difficult to work with or less ideal than using fuels as a coolant instead in small scale engines (<7000lbs of thrust/ Rutherford size and smaller) and how have people like Launcher (most notable example as they have recently made a partially LOX-cooled engine using modern manufacturing and modeling techniques) and research organizations overcome said issues in engines?
To answer your first question: one of the main problems with using the oxidizer in general is oxidizing of the cooling channels. Any hot oxidizer has this problem, but oxygen definitively has this issue to the extreme, which is why earlier engines using the oxidizer as regenerative coolant have been with different oxidizers than oxygen (see for example the hydrogen peroxide in the Black Knight engines)
Not too much is known about the Launcher e-2 design, but note that it uses both oxygen and fuel cooling. I assume the cooling channels being made from copper will help a lot, because despite copper obviously oxidizing and CuO having 1/10th of the thermal conductivity of most copper alloys, this oxidation layer is often too thin too have a very significant impact.
Another concern NASA had when they tried to make oxygen cooled engines, is that oxygen would leak through cracks into the the thrust chamber and affect the flow and/or chemistry, which could melt the inner wall. Here they outline their plan on testing these problems, but they ultimately resulted in melting the engines anyway, despite believing that it wasn't due the oxygen flowing through cracks, which was published here.
Do realize Launcher has only tested a scaled model so far, despite the info they give being very impressive and it looking awesome. Proof of concept small lox cooled engines were already made in 1981 (paper), so the development of Launcher needs to be a bit further before we can say they have completely figured out lox regenerative cooling.
I couldn't find any more recent papers, probably because there hasn't been too much research into it, but also because this type of knowledge is almost never made public.
Not very satisfactory, but the simple answer to the second question is: we don't know.