I think this deserves its own thread. I hope you start it. I really want to see the debate on this.
I disagree with you on first innings average, but that's really besides the point (I'm a subscriber to 3rd/4th innings average myself in trying to save games and getting real wins).
But that's a much less interesting debate than consistent 50's, or 100, 0, 0, 0, 0, 200 in what leads to more wins or less losses.
You've segue'd into something that serves its own thread. Like I say, I'd start it myself, but I'm loaded on infraction points. And I think you're on to a real debate, but I warn you, you're against popular opinion and cricket dogma (which I suspect was just to stop batsmen throwing their wicket away when they had a score and to keep going).
We can talk here, unless you feel it's essential to create a new thread.
The best way to look at it is this in my view. If all your batsmen were that inconsistent you'd be losing more often than winning. Hitting big runs doesn't guarantee the win, it's possible to bat out a draw still for the opponent. If you make no (few) runs you are almost guaranteed to lose. If you are consistent then you give your team a chance to win games more often, there are 10 other players out there. You can't win a test match on your own.
I understand are a subscriber of saving games, but as test cricket is played over an aggregate of two innings. When the batsman scores the runs isn't that relevant, just that his match aggregate is a stronger one than the opposing man. If Root scores 104 for England and Williamson scores 100 for NZ, then Root has contributed more to the side. If you have a top six of Root's they are making 624 per game, Williamson 600. Root's giving his bowlers 24 runs extra to defend over the game and they are coming at a faster rate (It would take the Roots 11.8 overs less to compile 24 extra runs). I know it seems basic, but I really think it is that basic personally in this particular case. Runs rule the roust in test cricket for batsmen. Root and Williamson can't directly change what the other 10 men do. It's a team sport and can never be proven how what they do effects their team mates. Therefore we are left to compare them on an individual basis towards the team, with numbers and historical form.
Ideally if you did have inconsistency it would be weighted towards the first innings in my view like Root to create scoreboard pressure for the bowlers and fielders. It also means the rest of your batters bat in both innings under less pressure as they come in with more runs on the board. The tail in particular wilts under pressure with the bat, so you want to get runs on the board early (to take pressure off your own tail and heap pressure on the opposing teams top order and tail in the first innings if you win the toss and bat). That's just my view on that however.
If all your players were consistent, not only would you win more but you'd be almost impossible to ever beat. Where Root and Williamson could fit in sides of varying strengths becomes another debate. It also moves away from comparing their individual abilities and contribution towards a properly built team unit. To fully assess this we must ignore their bowling (they wouldn't bowl an over in a proper team, certainly not a stacked one) and just gauge the disparity in their fielding. Root has taken 80 catches in 69 games. Williamson 58 in 65 games. Therefore if anything the Roots also bolstered by adding a ittle extra in the field in tests (and in fact in limited overs cricket too statistically).
In the long term the team with Roots as a top 6 would beat the Williamsons more often (assuming the same keeper and bowlers on both teams) due to the above. Which kind of puts to bed the debate of them head to head as individuals in my view.