I have never completed an appraisal where my opinion of value for a subject was different than what I concluded and reported in my appraisal. I am, and expect to remain, 100% accurate in that regard, forever. To argue otherwise is to make the case that you have been misleading.
If appraising were exact, we would not talk about opinions of value and define things in terms of opinions of value. Others would talk about calculated values and others would program their computers to calculate those values. Appraisers would have no use and no value. Arguing that appraisals could be exact ignores the daily occurrence where very similar to nearly identical properties sell for different prices. Each transaction has different, mostly human, buyers and sellers with different motivations and knowledge/advice and experiences and financial wherewithal. Humans being human, there will never be two identical transactions, even if the properties were identical. And there is not enough time and money to verify and measure every difference between every buyer and every seller in every transaction and then develop the impact those differences had on each transaction price. Teams of phycologists and valuation experts and lawyers and many others would be necessary in each attempt, and the outcome would likely be little better than competent, ethical appraisers can do.
Many argue that reporting a range in values would be more useful. To whom? Lender likely rely on a point value because their regulations and programs rely on "the" appraised value. If you give them a range, what will they use? Borrowers will likely argue for the highest every time. Conservative lenders (if they exist) and lenders who keep loans in house and understand risk will likely prefer the lower end more often. And who will determine what value is used in calculating "loan to value" ratios? Will all those benchmarks be revised to state $X +/- 5% or $X +/- 15% or whatever range is suggested in the appraisal? Will that be based on the center of the range, or the upper end of the range, or the lower end of the range?
And what is "a certain confidence level"? Just a statement by the appraiser that will be more meaningless than a point value will ever be? If not, then how is it measured? How is it calculated? How is it's credibility gauged? How is it reviewed?