Breaks that are part of the logical structure like section titles typically are not followed by indentation. The text is always a new paragraph. But page breaks and inserted floating tables etc are "unnatural" breaks forced by the physical page size, they may occur between paragraphs or mid-paragraph and are unrelated to the logical structure of the text.
Technically in TeX this pagination and float insertion happens after all the linebreaking has laid out the paragraphs into a sequence of lines with a paragraph indent and it is not possible to go back and re-flow the lines based on the page breaking. It is probably possible to implement some complicated multi-pass system that records paragraph starts in the aux file and tries to change the line breaking on the next run.
Such a scheme though would be confusing for readers. In a document using paragraph indentation you should be able to look at any part of the text and know if it starts a paragraph. With the proposed scheme it will be impossible to tell if the first line of the page starts a new paragraph or the page broke in the middle of a paragraph. Well you may be able to tell from the actual text, but the typography is supposed to help not make that harder.
Note the above comments apply to automatic page breaking. It is possible to have vertical spaces forcing logical breaks in the text, you may view such a break as an empty unnumbered section title and handle the (non) indentation in the same way, using the \@afterheading command that LaTex internally uses after section headings:
\documentclass{article}
\makeatletter
\newcommand\myspace[1]{\addvspace{#1}\@afterheading}
\makeatother
\begin{document}
\section{zzzzz}
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\myspace{1cm}
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\end{document}
parskippackage.