Men in committed, romantic relationships have lower testosterone

It's a peer reviewed paper, by actual researchers and scientists. I'm 99.99% sure they are aware that correlation isn't causation.

Furthermore, nowhere in the abstract does it draw any conclusions at all, it merely gives the results. The only people drawing conclusions are you and the other people posting tired cliches.

This is one study examining a theory which we have various lines of evidence for. It is not supposed to prove the theory - just test one prediction. It is not supposed to be the end of research on this topic. It is not supposed to be final. Criticizing it for any of those things is a demonstration that you do not understand how science is supposed to function.

For some of the background on this particular theory I highly recommend reading https://www.psychologytoday.com/blog/evolution-the-self/2009... and the follow-up https://www.psychologytoday.com/blog/evolution-the-self/2009.... (If you want to get to the point, it is probably better to start with the follow-up.)

Instead it is seeking to determine "[...] whether being in such a relationship (rather than being married) is the meaningful predictor of male testosterone levels."

Emphasis on meaningful predictor.

Of course testosterone drops when you find a mate. You don't have to fight for one any more.

They go on to show that it further decreases when you have children. Since virility is affected by T levels, it's a good hypothesis that having kids is likely a trigger to reduce the risk-seeking behavior in males after children are born.

It's kind of a "no duh" result in that light, and they sought to find evidence that supports this hypothesis. However, they are clear to state that they cannot address causation directly.

"High-T men may be less likely to enter stable, romantic relationships. Additionally, affiliative interactions with a partner may decrease T levels, in turn reducing mating effort. We also expect T variation within the group of paired men to be consistent with variation in mating effort, although we are not able to test this with our data set. For example, it may be that paired-male T levels will be highest during times of sexual activity with a partner (as suggested in Hirschenhauser et al., 2002) or that variation in the strength of the pair bond might explain variance in T levels among paired individuals. These are all topics for which longitudinal data would be of great help in teasing apart cause and effect."