Despite the fact you are visual, clear of cloud and can see the runway, you're going to now conduct a missed approach and attempt the whole thing again?
The rest of us are going to circle, going as low as 300ft above obstacles (not comfortable, I know) and land on the runway we initially intended to.
It's called the professional responsibility of a pilot to obey the law. If you descended below the charted circling minima while still in cloud, became visual at a lower level, and then proceeded to circle with me as a passenger, I would have very strong words with you on the ground (should we make it) and file a report.
What about airports like Kingaroy (only one that comes to mind, I'm sure there are plenty of others across the country)? The only approach (excluding RNAV) is the NDB rwy-16 (runway aligned). Based on some people's theories it might be impossible to use the airport if wind conditions did not allow a landing on 16.
If the only approach is a runway aligned approach - and there is no charted circling minima - then you may definitely NOT use this approach to the runway minima and then circle. In this instance, circling is prohibited.
There is a world of difference in (by day) being permitted to descend slightly below the cloud base, to ensure that you can remain visual while circling and maintaining visual obstacle clearance, and
making up your own minimum cloud base based on a visual appreciation of 300 feet.
If this has failed to convince you - consider this: this only matters in two instances
- When you fail your IFR renewal by attempting to kill your examiner
- When you crash, survive, and the judge is examining what THEY think "equal to or better than those specified for circling" is!
Good luck in trying to convince the judge that the Black & White printed minima in front of him are NOT "those specified", and your made-up-on-the-day "I can see the ground" conditions are.
NB: In a jet, the question is moot, as the aircraft is configured in the landing configuration (ie landing flap) for a runway approach, and is thus not able to safely circle.