"Retrotemporal" side effects (of centering, et al.)

A paragraph is broken in to lines based on the settings at the end of a paragraph so if you use centering mid-paragraph it affects the whole paragraph including earlier text.

Here centering is used just before the end of the paragraph but it is all centred.

documentclass{article}

begin{document}

fbox{Some long text that doesn't break} one fbox{Some long text that doesn't break}
fbox{Some long text that doesn't break} two two fbox{Some long text that doesn't break}
fbox{Some long text that doesn't break} three three three fbox{Some long text that doesn't break}
centering

end{document}

Note however the first line isn't quite centred as it has a paragraph indent on the left, parindent is set to 0 by centering but it is used too late here to affect the indentation box which has already been added.

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It is hard to address your comments about paragraph: in the standard styles it is a run-in heading set within the first line of the paragraph so can not be centred.

To have centred paragraph headings you would want to make it a display heading.

documentclass{article}

begin{document}

section{Intro}
Section text
subsection{Something}
SubSection text
subsubsection{Other thing}
SubSubSection text
paragraph{4th level heading} 
Paragraph  text
end{document}

You can adjust the paragraph layout:

documentclass{article}

makeatletter
renewcommandparagraph{@startsection{paragraph}{4}{z@}%
                                     {-3.25ex@plus -1ex @minus -.2ex}%
                                     {1ex}% %inverting the signs so a display heading
                                     {normalfontnormalsizebfseriescentering}}% centering
makeatother
begin{document}

section{Intro}
Section text
subsection{Something}
SubSection text
subsubsection{Other thing}
SubSubSection text
paragraph{4th level heading} 
Paragraph  text
end{document}