How do you know Anderson would have beaten Takase most of the times? Did you watch the fight? That was no fluke. That was a total domination from begining to end. Your statement is completely baseless.
You know who also beat Anderson and had record of 7-4? Ryo Chonan. Again, proving styles >>>> records.
Records are only indicators, but they're not the best indicators to predict a fight. They're better used to assess a fighter's overall success in MMA, but not how that particular fighter matches up against a wrestler or striker. They don't give any insight in any of the variables that happen inside the ring. They don't show strenghts and weaknesses. They just tell who was won and lost more.
Records are quantitative information. Styles are qualitative. When you want to understand how something works, and why it works the way it works, you need qualitative knowledge. Fights aren't numbers. Fights are a bunch of variables meeting each other. To better understand a fight you have to study the those variables because the numbers won't tell you anything about the fight itself.
About team sports, if the higher ranked teams (and thus with better numbers) lose to lower ranked teams, that's pretty much proof numbers are not being reliable. On the other hand if you study variables, suchs the teams' weaknesses, strenghts, injuries, fatigue, etc. you might have a better idea of the outcome. Eg. Germany lost to Mexico in the world cup. It was considered a big upset, as Mexico had never beaten Germany in a world cup. However if you saw Germany in the preparation matches, you would know they were playing terribly, whereas Mexico has always been known as a team that plays better when they're underdogs. To anyone who acknowledged these variables, the result wouldn't have been nearly as surprising compared to the person who only looked at the numbers.
I agree that a lot more than records are needed; as you say, there are a lot more variables involved. Where I disagree is what is the single most indicative indicator.
Suppose we were only give one piece of information about a fighter. You could choose their record (including the organizations in which they fought, as that's part of the record). Or you could choose their style but with no info about their record. Or you could choose their physical attributes, but no info about their record, style, or skill level. Or you could choose their skill level, but no info about their record, style, or physical attributes.
The advantage of the record is that (admittedly to a limited extent) takes the other factors into consideration. A guy with say a 20-0 record in the UFC is going to have pretty decent skills, a fairly flexible style, and at least reasonable physical abilities.
Whereas you could have a guy with a good style matchup against a UFC striker (say a wrestler against Daley back in the day), but who was a weak guy with a 0-20 record in some minor organization. Or a guy with excellent skills, but with a 0-20 record because of physical or mental weaknesses. Or a guy with great physical attributes with a 0-20 because of lack of skill or a horrible style (run the opponent throwing wild punches until exhausted).
Record isn't enough by itself, but it encompasses the other elements better than any other single indicator.
Even when you point out that Takase with 4-7-1 beat Anderson, you're unconsciously using his record to note he fought in Pride, a top level organization. Would you bet on a guy with Takase's style but with a 4-7-1 record in some tiny local organization, against Anderson?
In terms of team sports, you're right that records aren't that useful for single game predictions -- any team (at least in the pro's) can beat any other team on a given day. Where they become useful is when you get a statistically meaningful number of games (baseball in fact, with its 162 game season, because very statistical -- so much so that many fans say its ruining the game, though that's a different topic). That's why many team sports have best of seven series (well, that and because the owners love the play-off fan money). Anyone can win a single game, but the teams with better records tend to win the seven game series.
The problem with soccer (at least World Cup soccer) in that regard is the teams only play each other once. Looking at Germany and Mexico over decades of World Cups gives no useful information, because the teams from even two decades ago have no players in common (and in fact, most teams seem to change a majority of their players over a single decade). How 1960 Mexico did against 1960 Germany tells us nothing about how 2020 Mexico would do about 2020 Germany, they're completely different teams.
Of course, that means record is completely meaningless for World Cup soccer, as you point out. But that's not typical for team sports. In professional soccer (say premier league in England or the Bundesleague in Germany), do teams play each other more often in a season?