Making adjustments based on biblatex style
It seems I needed Aristotle to save my project -- with the help of Saving Aristotle: How can Biblatex redefinitions be made conditional on the style selected? the code can me massively simplified to the following example:
\documentclass{beamer}

\usepackage[
%   style=numeric,
%   style=numeric-comp,
%   style=numeric-verb,
%   style=authoryear,
%   style=authoryear-comp,
%   style=authoryear-ibid,
   style=authoryear-icomp,
]{biblatex}

\addbibresource{biblatex-examples.bib}% included in full tex distributions or from http://mirrors.ctan.org/macros/latex/contrib/biblatex/doc/examples/biblatex-examples.bib

\makeatletter
\newcommand{\fixnumericstyles}{%
    \setbeamertemplate{bibliography item}{\insertbiblabel}
}

\newcommand{\fixauthoryearstyles}{%
    \newlength{\beamer@bibiconwidth}
    \settowidth\beamer@bibiconwidth{\usebeamertemplate*{bibliography item}}
    \setlength{\labelwidth}{-\beamer@bibiconwidth}
    \addtolength{\labelwidth}{2\labelsep}
    \addtolength{\bibhang}{\labelsep}
}

% from https://tex.stackexchange.com/a/365563/36296
\def\beamer@blx@splitfile#1-#2\@null{#1}
\edef\beamer@blxbase{\expandafter\beamer@blx@splitfile\blx@cbxfile-x\@null}
%
% numeric styles %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\edef\beamer@namenumeric{numeric}
\ifx\beamer@blxbase\beamer@namenumeric
    \fixnumericstyles
\fi
%
% author year styles %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\edef\beamer@nameauthoryear{authoryear}
\ifx\beamer@blxbase\beamer@nameauthoryear
    \fixauthoryearstyles
\fi

\makeatother
\begin{document}

\begin{frame}
\cite{sigfridsson}
\printbibliography
\end{frame}

\end{document}

Update 2020
In the mean time, the biblatex developers were so nice to add some hooks which can be used for this purpose, see https://github.com/plk/biblatex/pull/973 for more details. This simplifies the solution dramatically and makes it much more versatile.
The following code was added to beamer to make the necessary adjustments:
% Adding patches to some biblatex styles
\csappto{blx@filehook@postload@numeric.bbx}{%
  \mode&lt;presentation&gt;{\setbeamertemplate{bibliography item}{\insertbiblabel}}}
\csappto{blx@filehook@postload@alphabetic.bbx}{%
  \mode&lt;presentation&gt;{\setbeamertemplate{bibliography item}{\insertbiblabel}}}  
\csappto{blx@filehook@postload@authoryear.bbx}{%
  \mode&lt;presentation&gt;{%
      \newlength{\beamer@bibiconwidth}
      \settowidth\beamer@bibiconwidth{\usebeamertemplate*{bibliography item}}
      \setlength{\labelwidth}{-\beamer@bibiconwidth}
      \addtolength{\labelwidth}{2\labelsep}
      \addtolength{\bibhang}{\labelsep}
  }}  
\csappto{blx@filehook@postload@authortitle.bbx}{%
  \mode&lt;presentation&gt;{%
      \newlength{\beamer@bibiconwidth}
      \settowidth\beamer@bibiconwidth{\usebeamertemplate*{bibliography item}}
      \setlength{\labelwidth}{-\beamer@bibiconwidth}
      \addtolength{\labelwidth}{2\labelsep}
      \addtolength{\bibhang}{\labelsep}
  }}