In reference to your point, In particular, has copy-paste of mathematics been implemented so that it may be used without disadvantages
I don't know the particulars of what you cite, but the accsupp package allows different things to be displayed in a PDF versus what shows up in a copy paste.
REVISED SOLUTION (using Raphael's suggestion of \detokenize)
It would seem that \detokenize alleviates the need for separate arguments for the typeset and actual-pdf text, which will greatly streamline the use of this approach. I extend my thanks to him.
I also show how this even works for \displaystyle math.
\documentclass{article}
\usepackage{accsupp}
\newcommand\copypaste[1]{%
\BeginAccSupp{method=escape,ActualText={\detokenize{#1}}}%
#1%
\EndAccSupp{}%
}
\begin{document}
What I have is \copypaste{$x^2 + y^2 = z^2$} and \copypaste{$\frac{1}{2}$}.
Try to copy/paste me.
\copypaste{\[
y = \frac{\cos{x}}{1+\cos{x}}
\]}
Here it is with no copy/paste tuning: $x^2 + y^2 = z^2$ and $\frac{1}{2}$.
\[
y = \frac{\cos{x}}{1+\cos{x}}
\]\end{document}
Here is the PDF's appearance:

Now, when I go into Adobe Reader on the produced PDF file and hit ctl-A ctl-C to copy the whole document, the paste into a text file will appear as:
What I have is $x^2 + y^2 = z^2$ and $\frac {1}{2}$ . Try to copy/paste me.
\[ y = \frac {\cos {x}}{1+\cos {x}} \]
Here it is with no copy/paste tuning: x2 + y2 = z2 and 1
2 .
y =
cos x
1 + cos x
1
ORIGINAL EDITED SOLUTION to allow optional argument with different "ActualText" content, for example, to use \noexpand for certain math arguments.
\documentclass{article}
\usepackage{accsupp}
\newcommand\copypaste[2][\relax]{%
\ifx\relax#1%
\BeginAccSupp{method=escape,ActualText={#2}}%
#2%
\EndAccSupp{}%
\else%
\BeginAccSupp{method=escape,ActualText={#1}}%
#2%
\EndAccSupp{}%
\fi%
}
\begin{document}
What I have is \copypaste{$x^2 + y^2 = z^2$} and
\copypaste[$\noexpand\frac{1}{2}$]{$\frac{1}{2}$}.
Try to copy/paste me.
Here it is with no copy/paste tuning: $x^2 + y^2 = z^2$ and $\frac{1}{2}$.
\end{document}