A perfect query optimizer should make the best plan if provided with a full sample of statistics. But even a perfect optimizer does not need the information provided by a full sample of statistics to make the best plan. A simple example:
Assume that for this table tab1 there exists a nonclustered index on col1. The optimizer has to possible plans:
1) scan the whole table and check for each row if
col1=3 and col2=4
2) consult the index to find the position of all rows in the table with col1=3. Lookup each of these row in the table and check if
now assume the table has a size of 123,456 GB and 1 123 456 789 rows and 567 890 123 of them (about half of them) have
col1=3. What should the optimizer propose? It schould propose a full table scan. The other possibility, looking up 567 890 123 rows one by one is too expensive.
Now assume the optimizer only has a rough estimate of the table data: the table size is about 100GB, there are about 1,000,000,000 rows and about 600,000,000 of them have
col1=3. Based on this information the optimizer will choose the same good plan as in the first case.
The decision is based on the size of the ratio
100*(# of col1=3-rows)/#(all rows) and if this value is larger 10% (I don't know which value is really used) the full table is scanned. The decision is not based of the size of the 5th place after the decimal point of the ration.
In a special case where the exact ratio is 10,00001% and the ratio based on the rough estimate is 9,99999% the optimizer will choose different plans but maybe for these different plans the execution time may be the same for both plans or may be better for the plan based on the rough estimate
Administrative jobs like calculationg statitistics should be done only with least resource consumption that is possible. Therefore only the precision that is necessary should be tried to be reached.