Why not do both? The answer is cost.
The HBA1c did not start out as a test to diagnose Diabetes. It was used primarily to monitor the glucose control of diabetics over a 3-4 month period. It measures the % of hemoglobin in the body that are glycated (ie have attached glucose molecues). The life span of red blood cells is about 120 days. Hence the variations in HBA1c will not change day to day but over a period of 120 days or so.
Our target for diabetics is a HBA1c of <7% for adequate glucose control.
The way to diagnose diabetes was to do a fasting blood glucose sample. If it was >7.0 we would repeat it again and if was still >7.0 we could diagnose Diabetes in the patient. Another test was the random blood glucose level (non fasting). A reading > 11.0 suggested diabetes. The key is to have 2 separate readings. Eg either 2 abnormal fasting readings or 2 abnormal random readings or 1 abnormal fasting and 1 abnormal random. 2 abnormal = diabetes. To complicate things a bit there is pre-diabetes as a diagnosis now. Fasting blood glucose of 6.1-6.9 is considered possible impaired fasting glycemia and hence pre-diabetes.
We can also send patients for a glucose tolerance test where they fast for 8 hrs , then get a fasting sample taken, then drink a 75g glucose drink, wait 2 hours and have their blood glucose drawn again. The 2hour reading if >11.1 supports a diagnosis of diabetes. (of course their fasting might already be >7.0 but some people have normal fasting but abnormal 2 hour post prandial readings). If the 2 hour reading is between 7.8-11.0 it suggests impaired glucose tolerance which is also part of the pre-diabetes spectrum.
In recent times, the HBA1c has been used to diagnose diabetes as well. A reading of <6.0 is considered normal. If it is >6.5 it suggests diabetes. Between 6.1 to 6.4 might suggest pre-diabetes.
Again you need 2 abnormal results to diagnose diabetes. Eg say someone has HBA1c of >6.5 and fasting glucose >7.0 then you can diagnose DM. The advantage with adding the HBA1c to the fasting glucose is you might not need to repeat another fasting glucose. That's about it.
Cost is the catch. And you know lah, in Singapore cost is the big thing.
The HBA1c used to cost around $25-$35. Fasting glucose is very cheap. I think like $2-$5. Maybe even cheaper. So 2 fasting glucose readings is still cheaper than HBA1c alone. And if you are trying to DIAGNOSE diabetes there is no real case for using HBA1c besides convenience to the patient. It is no more "accurate" than doing 2 fasting glucose readings or a glucose tolerance test.
But HBA1c is essential in determining a diabetic (already diagnosed) patient's long term glucose control.
Hope this clarifies some of the questions.
In canada we do both the HBA1c and Fasting glucose in screening.