Why does supertabular put the page break early in all kinds of situations?

In this MWE, supertabular breaks the page (or column, if one is using twocolumn) early. In fact, the first page holds only 5 lines, while the second holds 7.

documentclass[twocolumn]{article}
usepackage[paperheight=2in]{geometry}
usepackage{supertabular}
begin{document}
begin{supertabular}{p{3mm}}
    1 2(  3 4(  5
    1 2 3 4 5 6 7
end{supertabular}
end{document}

I thought his may have something to do with the presence of the parentheses, but I can reproduce a less severe issue (6 lines vs. 7) without them as well:

documentclass[twocolumn]{article}
usepackage[paperheight=2in]{geometry}
usepackage{supertabular}
begin{document}
begin{supertabular}{p{1.7mm}}
    1   2 3   4 5   6
    1 2 3 4 5 6 7
end{supertabular}
end{document}

In my document, I can even reproduce the issue without any parentheses or line breaks in cells. That is a bit harder to reproduce as an MWE, however.

I have tried the approach described in Prevent xtab breaking table too soon and Prevent supertabular* from breaking too early without success.

Edit: Here’s another example not involving line breaks in cells, but a line break in the tablehead:

documentclass[twocolumn]{article}
usepackage{lipsum}
usepackage{supertabular}
defheads{Head Head Head Head Head Head }
edefmycont{headsheadsheadsheadsheadsheadsheads}
tablehead{multicolumn{1}{p{dimexpr columnwidth - 12pt}}{mycont}}
begin{document}
lipsum[1-2]

begin{supertabular}{p{1cm}}
    123456789
    123456789
    123456789
    123456789
end{supertabular}
end{document}

Here’s one using tablefirsthead (in this case, it seems the second column is long, rather than the first too short – but they should have the same length anywy, and I don’t get a box warning, either):

documentclass[twocolumn]{article}
usepackage{supertabular}
tablefirsthead{}
tablehead{Continued}
begin{document}
begin{supertabular}{p{1cm}}
    123456789
    123456789
    123456789
    123456789
    123456789
    123456789
    123456789
    123456789
    123456789
end{supertabular}
end{document}

And here’s one using tablecaption:

documentclass[twocolumn]{article}
usepackage{supertabular}
tablecaption{Caption}
begin{document}
begin{supertabular}{p{1cm}}
    123456789
    123456789
    123456789
    123456789
    123456789
    123456789
    123456789
    123456789
    123456789
end{supertabular}
end{document}

Edit 2:
I also found Too large bottom margin with xtab (or supertabular) and Long tables (spanning multiple pages), put side by side and tried their solutions.

I need twocolumn, so longtable won’t work; and the best solution for the first link is even worse:

documentclass[twocolumn]{article}
usepackage{lipsum}
usepackage{xtab}
usepackage[nofoot]{geometry}
tablefirsthead{}
tablehead{H}
begin{document}
begin{xtabular}{p{1cm}}
    123456789
    123456789
    123456789
    123456789
    123456789
    123456789
    123456789
    123456789
    123456789
end{xtabular}
end{document}

I think my summary question is: is this fixable at all, or should I refrain from using supertabular/xtab if I want my tables to break correctly?

documentclass[twocolumn]{article}
usepackage{lipsum}
usepackage{supertabular}
usepackage{showframe}

% https://www.guitex.org/home/forum/5-tex-e-latex/26889-supertabular-e-twocolumn-riempimento-parziale-altezza-testo?lang=it#26893
makeatletter
defmod@estimate@lineht{% 
  ST@lineht=arraystretch baslineskp
  %globaladvanceST@lineht by 1p@ 
  ST@stretchhtST@linehtadvanceST@stretchht-baslineskp
  ifdimST@stretchht<z@ST@stretchhtz@fi
  ST@tracetw@{Average line height: theST@lineht}% 
  ST@tracetw@{Stretched line height: theST@stretchht}% 
}
newenvironment{strictsupertabular}
  {letestimate@linehtmod@estimate@linehtsupertabular}
  {endsupertabular}
makeatother

begin{document}

tablefirsthead{}
tablehead{H}
begin{strictsupertabular}{p{1cm}}
    123456789
    123456789
    123456789
    123456789
    123456789
    123456789
    123456789
    123456789
    123456789
end{strictsupertabular}
end{document}