Your blood sugar, as well as other blood markers, are in equilibrium most of the time.
A meal will create a rise in glucose, but this will only last about 2 hours, so that you will have raised glucose only 6 hours out of 24. So this is one reason why the fasting glucose is the glucose to which your body is exposed most of the time.
But more important, the doctors don't care for your peak glucose levels, they care for the equilibrium level of your glucose homeostasis, and that's 5 mmol or somewhere very close to it. If it is not there, then the mechanism for achieving it is broken, no matter what your postprandial glucose levels are. So both of your assumptions are incorrect.
And if you are on a diet which has your blood glucose levels constantly elevated, that's a very calorie dense diet and you are probably indeed in trouble. But even then, measuring your fasting glucose is important, because the doctor cannot make any conclusions from the raised levels.
By the way, there is also another test for blood sugar which gives you an estimation of not the current blood sugar, but of the average blood sugar over the last few weeks. Both an elevated fasting glucose and an elevated hgb 1ac levels are diagnostic criteria for diabetes, so if you somehow managed to keep your fasting glucose low but your average glucose unreasonably high, this could be discovered and you will be diagnosed with diabetes or warned that you are in a prediabetic condition, depending on the current diagnose guidelines used in your country. But if you suspect this, you should probably inform your physician, as I don't think hgb a1c is measured in routine blood tests.
Source: a Coursera course on diabetes I can't link because it's no longer open, sorry. Maybe somebody else has a linkable source and can edit it in.