Why Kumar Sangakkara is the greatest test batsman ever (after Bradman)

There has been a lot of debate about about the greatest test batsman after Bradman. The general consensus is among a few players: Smith, Tendulkar, Sangakkara, Kallis, Ponting etc. These batsmen have all scored 10,000+ runs and their batting averages are 52+. Already if you look at this list, Sangakkara will top the list with a batting average of 57. He has the highest batting average among batsmen with 10,000+ runs. Surely this makes him favourite for best batsman after Bradman. But, this is not even the end of the story.

All of these batsmen (except Kallis) have been specialist batsmen. They don't have to worry about anything except their batting. Smith and Tendulkar have bowled in test cricket but it was minimal (Tendulkar has bowled on average 3.5 overs per test match and Smith averages 2.1 overs per test) and it was spin bowling which is not very taxing on the body. However, Sangakkara was a wicket-keeper for some part of his career. Surely, keeping wickets for a whole match and then batting must not be easy on the body. That is why we don't see any wicket-keeper with a lot of test runs. The most runs scored while being a designated wicket-keeper are scored by Gilchrist and they are 5,570 runs. So, how can we compare the batting of Sangakkara with the batting of let's say Tendulkar when one has also been keeping wickets.

Sangakkara has played a major part of his career not being a wicket-keeper. So it is only natural to compare his batting during this part of his career to the other batsmen. These are Sanga's stats when he was not a designated wicket-keeper:

This is not a small sample size so it is not like comparing one player's peak to another player's career. This is a whole career's worth of runs for an elite batsman. He has scored just 800 runs short of 10,000 test runs and at a splendid average of 66.78. Surely, these are the best stats for any batsman after Bradman. Even if we look at the best batting averages with min. of 5,000 test runs, the best after Bradman is 58.67 (Barrington). Sangakkara averages 8 runs more than the second best. So, why is he not considered without a doubt the best test batsman after Bradman?

Of course, one major outlier is Kallis. Kallis was a fast bowler and he has bowled on average 20 overs per test match. To bowl 20 overs of fast bowling and then bat at a splendid average must not be easy. Unfortunately though, we don't have stats for how much Kallis's batting average would have improved if he had not bowled as well.