{
\def \l {\mathrm{l}}
\def \r {\mathrm{r}}
\def \Bl {\mathrm{Bl}}
\def \Br {\mathrm{Br}}
\def \B {\mathrm{B}}
\def \nIIom {n_{2\omega}}
\begin{equation}\label{eq:interface_conditions}
\begin{aligned}
F_{1\l} &= F_{2\r} + F_{2\l} \exp (i\,k_2 L) + F_{\Br} + F_{\Bl} \exp(i\,k_\B L) \\
F_{1\r} &= -\nIIom \, F_{2\r} + \nIIom \, F_{2\l} \exp (i\,k_2 L) - \nIIom \, F_{\Br} +
\nIIom \, F_{\Bl} \exp(i\,k_\B L)\\
F_{3\r} &= F_{2\r} \exp (i\,k_2 L) + F_{2\l} + F_{\Br} \exp(i\,k_\B L) + F_{\Bl} \\
-F_{3\l} &= \nIIom \, F_{2\r} \exp (i\,k_2 L) + \nIIom \, F_{2\l} -
\nIIom \, F_{\Br} \exp(i\,k_\B L) + \nIIom \, F_{\Bl}
\end{aligned}
\end{equation}
}
(by the way the formula may contain some math mistakes---it is supposed to represent interface conditions for a system of waves in a nonlinear optical medium---but it is good enough for showing the editing point) F_{1\mathrm{l}} &= F_{2\mathrm{r}} + F_{2\mathrm{l}} \exp (i\,k_2 L) + F_{\mathrm{Br}} + F_{\mathrm{Bl}} \exp(i\,k_\mathrm{B} L)
...
The obvious objection is that of course most people do use macros. But that's the point: every LaTeX document ends up being its own impenetrable language.On the other hand, you don't write complicated mathematical equations quickly if you've got any sense anyway.
I don't get this line of reasoning. Writing equations is hard, so what difference does it make if you make it a lot harder? I think the fact it's hard makes it even more important to make it easier to write!
Proofreading / editing (as opposed to writing) is even more severe. When using raw LaTeX, there's absolutely no way you can be sure the equation is right without checking the PDF, so you end up in a slow loop of typesetting (the whole document!), read something for a while, go back to the LaTeX to fix something you've found, spend a while finding where the problem is, etc.; in LyX you're just organically reading and editing the document. If you spot an incorrect subscript, you just click on it and fix it then carry on reading. In raw LaTeX that can 100 times as long, or even longer still if you take into account the context switch of your mind.