pgfplots .provide style similar to tikzset's .provide style

Question

I have been using tikzset{style name/.provide style={}}from Is there something like \providetikzstyle similar to \providecommand? defined as

\tikzset{/handlers/.provide style/.code={%
    \pgfkeysifdefined{\pgfkeyscurrentpath/.@cmd}{}%
        {\pgfkeys {\pgfkeyscurrentpath /.code=\pgfkeysalso {#1}}}%
}}

and have found it very handy. What is the similar version for \pgfplotsset. The following does not seem to work:

\pgfplotsset{/handlers/.provide style/.code={%
    \pgfkeysifdefined{\pgfkeyscurrentpath/.@cmd}{}%
        {\pgfkeys {\pgfkeyscurrentpath /.code=\pgfkeysalso {#1}}}%
}}

The MWE below produces the image on the left, but should produce the image on the right once .provide style is working for \pgfplotsset (ie, no x tick labels and a thick red box):

References:

• Is there something like \providetikzstyle similar to \providecommand?

Code:

\documentclass[border=2pt]{standalone}
\usepackage{pgfplots}
% https://tex.stackexchange.com/questions/22640/is-there-something-like-providetikzstyle-similar-to-providecommand
\tikzset{/handlers/.provide style/.code={%
    \pgfkeysifdefined{\pgfkeyscurrentpath/.@cmd}{}%
        {\pgfkeys {\pgfkeyscurrentpath /.code=\pgfkeysalso {#1}}}%
}}
%% How to define this???
\pgfplotsset{/handlers/.provide style/.code={%
    \pgfkeysifdefined{\pgfkeyscurrentpath/.@cmd}{}%
        {\pgfkeys {\pgfkeyscurrentpath /.code=\pgfkeysalso {#1}}}%
}}
\begin{document}
\pgfplotsset{tick label style/.provide style={% output should be as if this was ".style" instead of ".provide style"
    xticklabels={},
    draw=red, 
    ultra thick,
}}
%% This should be ignored as it was already defined above.
\pgfplotsset{tick label style/.provide style={
    xticklabels={},
    yticklabels={},
    draw=blue, ultra thick,
}}
\begin{tikzpicture}
\begin{axis}[%
    tick label style,% <---- y ticklabels shown, x ticklabels suppressed, axis in red
]
    \addplot {x^2};
\end{axis}
\end{tikzpicture}
\end{document}