Averaging and totaling are exactly equivalent things if no voter ever leaves a score blank (or if blanks are disallowed).
They only differ if some voters intentionally leave some scores blank (by filling in that slot with an X) because of their intent not to express an opinion about that candidate. Then with totaling, blanks would be equivalent to a zero-vote, whereas with averaging, blanks are ignored.
Claim: Averaging the scores of all those who expressed an opinion, leaving out blanks, is a bad idea, since it could elect an unknown based on a single vote!
Response: Yes, true in theory... (if we eliminate the "safety valve rule" and its current better version)... but you have to stop worrying about super-unlikely worst case scenarios and focus on cases that will happen.
The actual experimental fact is, lots and lots of voters experimentally are seen to fill in a "no opinion/ignorant" slot with zeros. Not all of them. But about 1.7 times more than prefer to leave them blank. (According to our data #82 here.) My inquisitor evidently feels the same way. (In fact it is quite astounding how those who furiously argue against the X-blank option assert that  they and their side – demanding that blanks be regarded as zero – are vastly in the majority in this argument, but  none of that vast majority is actually going to show up at the polls to actually vote 0, which is the whole reason we are going to get a catastrophe.) These "give 'em zeros to play it safe" voters will have a huge effect and will prevent the "single vote from causing a win" nightmare scenario. In fact they will prevent the "any small percentage of votes causing a win" scenario. It simply is a bullshit scenario that will not happen.
Can it happen? Yes, but it is unlikely. You do not seem to appreciate just how unlikely. So let's do a calculation. Let us suppose it is a 100-voter election. Let us suppose that the stealth candidate has 10 secret supporters pledged to give him 99s as part of his Evil World Takeover Plan. Suppose he needs above 49 average to get elected. Now suppose the rest of the voters (who are totally ignorant of that candidate) flip a coin. If "tails" they leave the slot blank to express their ignorance. If "heads" they fill it in with 0 to play it safe. This approximates the true situation, except I am being very generous to my inquisitor by using a fair coin. In fact, the data says the coin is biased about 10:17 in favor of heads. Maybe more. Ok, what are the chances the stealth candidate will be elected? Same chances the 90 coin flips come up heads only 10 times or fewer. I compute this chance to be 5.3×10-15. Suppose we held one such election every day from the beginning of the universe until now. The number of times the stealth candidate would have been elected, from then to now, would have been in expectation 0.025, i.e. you'd have to wait 40 universe-lifetimes for it to happen.
Or put another way, of all the elections (including counting informal votes at meetings and family gatherings) ever held in all human history, the total number that would elect the stealth candidate (at this rate) would be below 1.
Now I was very generous to my inquisitor in the above calculation. In reality any such stealth candidate could not mobilize 10% of society while at the same time keeping everybody else totally ignorant about him! One or the other, ok. But not both. And further, suppose we are not talking about a 100-voter election. We are more realistically talking about 1000, or 10000, or more, voters. Then the unlikeliness gets really incredibly huge. I mean 0.000000...0001 with pages and pages of zeros before you reach the 1. That is how unlikely. Beyond tiny. Even if an election were held every nanosecond on every atom in the universe for the whole age of the universe, the total number of stealth victories then would still be incredibly near zilch.
So can we return to the world of reality? Election system design should not be based upon ludicrously unlikely stuff. It should be based on likely phenomena. What is likely, is that honest voters and whatever they want to say, is good to get in as undistorted a form as possible.
Paranoia can be good. But overmuch paranoia, is counterproductive.
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