The point of the "Around Point" placement is to allow the label engine some freedom to optimize the placement of the label within the defined radius. This can help avoid overlaps/truncations when changing scale, or when other labels are set to move around the polygon's visible extent.
In application, I've found the performance of "Around Point" to be underwhelming, normally resulting in an almost entirely static placement strategy that does not help much, if at all, with overlaps/truncations.
However, there have been a large number of changes to the labeling engine in QGIS recently, all of which have been merged into QGIS Master/Nightly. I'm uncertain of what release they're targeted for at present. Nyall Dawson and others have been really digging into PAL and fixing many shortcomings, bugs, limitations, etc., with the outcome of a seemingly far more robust and performant labeling engine coming soon™.
Here's one that will likely vastly improve the usability of "Around Point" (as well as all other label rendering): Rework labeling maximum candidate logic #33496
First up, the easy one: This PR drops the setting for maximum number of point label candidates. This setting is easily replaced by automatically calculated, optimised values for each separate point placement mode individually. So that's an easy win.
Then the exciting bit: a rework of the label engine "maximum line candidates" and "maximum polygon candidates" settings and logic
The previous approach of a single fixed value which applied to ALL line and ALL polygon
features was... not ideal. It meant that all line features would be assigned the same
number of candidates, regardless of length. So a road of length 1 cm on the rendered
map would have an identical number of candidates as a 30cm road covering the length of the
whole map!! This resulted in both a lot of wasted calculations (generating a ridiculous
number of candidates for small lines at barely discernable distances from each other)
AND an insufficient number of candidates for lengthy features (resulting in worse label
placement for these features).
The situation was similar, but even worse for polygons. Checkout the screenshot below, showing how a tiny polygon is flooded with an excessive number candidates yet the larger polygon has comparatively poor coverage by its candidates:
Now, the setting is reworked to "Number of line candidates per cm" and "number of
polygon candidates per cm2". This means that small features get much less candidates,
and large features get much more features! Both a win for map rendering speed in many
circumstances AND good cartography... now that's a nice Christmas gift for QGIS :)
The new candidate placement is shown below. Note the reasonable candidate count for the small polygon, and better coverage of the larger polygon (a follow up PR will bring further dramatic improvements to this candidate coverage!)
Combined with this: Improve polygon candidate generation logic #33535
Instead of basing the initial dx/dy for the grid-based polygon candidate
generation on the size of the label itself, instead use either the
engine setting for polygon label density OR try and infer this from the
maximum number of candidates to generate for the polygon.
This avoids numerous issues with the label-size based approach:
small labels (e.g. 1-2 digit labels) would generate a HUGE number of candidates
because the initial dx/dy were very small
large labels would generate very few candidates, giving few options for
placement within these polygons (due to initially large dx/dy)
by generating much more candidates then desired for small labels,
all the candidates further from the polygon centers would be culled
at a later step, meaning that the only candidates available for the
labeling problem solving would be clustered around a very small area
of the polygon (instead of distributed over the whole polygon)
Please keep in mind that the list above is not exhaustive, but just shows two examples of significant improvements to PAL which should make labeling more effective across the board, including when using the "Around Point" option.