A planet is within 16 minutes of each angle for 2 minute and 8 seconds on average (depending on the rising time of the degree), but always for 8 minutes and 32 seconds with all four angles every day. Each planet is going to be within 16 minutes of an angle for 2.16 days over the year.
I`d say it would be easier to elect a chart with a planet both in domicile AND on MC.
If it shall happen while the planet is also in cazimi, it makes only a few minutes of an appropriate time in a year.
AND the latter option is impossible for Mercury and Venus, since these planets can be cazimi only in certain signs.
Saturn and Jupiter are going to spend a bit more than 12 hours in cazimi each year (because of their slow direct speed), Mars, Venus and Mercury as direct planets have almost 2 days (because they move along with the Sun), when Venus and Mercury are retrograde, they spend even less hours than Saturn and Jupiter (because they move in opposite directions). Thus the seven planets as whole in conjunction with the Sun are slightly more rare than in conjunction with the four angles, though Mercury and Venus individually spend slightly more time in cazimi.
They say "heaven can wait".
Humans can`t wait for the most appropriate time sometimes.
And humans are sometimes late.
Anyway, it seems that tHE EMPHASIS of a planet alone isn`t a guarantee of happily-ever-after.
The 16 minutes are arbitrary and do not have much to do with conjunctions per se, but rather with the average diameter of the Sun's disk.
Yes, but It`s easier to compare cazimi planet to a conjunction of a planet to an angle if the latter is within 16minute orb.