I was unaware of that feature and have just verified your behaviour. I’m running KiCad Win64 (5.1.2)-1.
I started with a regular text. The anchor point was lower left and color blue, both as expected.
I use the RMB menu convert to label.
The text goes black as expected but the square connection point never appears.
Hovering over the new label, I press M to move it and the cursor snaps to the lower left and the connection point appears. (The connection square not initially showing might be an indication of a refresh issue?).
After placing the label back down the label finally looks as expected.
Again using the RMB menu to convert, this time back to a text. The color goes to “text blue” of both the text and the square connection point.
Moving or editing the text doesn’t remove the connection point. Converting to any of the other types of labels and back to text doesn’t get rid of the square connection point. Even running ERC doesn’t clean the square connection point from the text. I put the square connection dot on a wire while it was text and it didn’t disappear as if an electrical connection was made, so I didn’t bother to create a netlist to see if the text was acting like a label. My guess is it isn’t acting like a label, but there is something that isn’t updated to remove the square glyph from the anchor point.
(Just out of chuckles, I did try with a multi-line text and the convert option in the RMB menu didn’t even show.)
Note, however, I did also find another potential issue. The text that I used has spaces, however one is prevented from using spaces when creating labels. Trying to convert a text with spaces should have probably thrown an error.
@svniceguy What say you report the bug about the connection square (reference this thread on the bug tracker for the devs to follow up) since you found it. I’ll report the “space in a label” issue since I found that one.