ENTER↑ is a misnomer, long live ENTER:

[Katie Wasserman]

Quote: But here the HP-35 designers overshot the mark—instead of just having ENTER^ terminate digit entry, they (who knows why?) made it also carry out the unrelated task of duplicating the number into the Y-register, then disabling stack lift.

I don't really know the answer to this, but being an original HP-35 user I thought (and still think) it was to make squaring easier. Since there is no x^2 function on the HP-35 using ENTER * does the trick. In the HP-35 manual they suggest doing exactly this (see page 12). To this day, I still square like this even on RPN calculators that have an X^2 function (well, unless I'm programming and need the extra stack level or memory space).