I came across a study on the usage of -tari constructions. I must admit I don't fully understand it, but here is what I could glean from the paper.
Typical constructions with only one -tari phrase instead of two can be used to set a situational frame, inviting the listener to focus on characteristics of a situation. Doing this can achieve the following effects:
- Softening
Example
しばらく彼と会ったりしないほうがいい。
It's better not to meet up with him for the time being.
Rather than「会わないほうがいい」which is a direct advice, using 「会ったりしないほうがいい」couches the specific advice as an example and has a cushioning effect.
- Emphasis
Example
彼女に払わせたりしませんよ。
There's no way I would let my girlfriend pay for this.
Adding 「たり」 implies that there are other examples along the same intention. However, the effect of omitting these other examples is to focus the listener’s attention on the characteristics of the specified action (perhaps from the speaker’s point of view letting a girl pay is not a 'masculine' thing to do) and in turn putting emphasis on the speaker's denial.
- Judgement
Example
どうしてあんな人を誘ったりしたんですか。
Why did you invite someone like him/her?
This can be extended from the previous function. By directing the listener to focus on the characteristics of the example provided (あんな人を誘う), it adds a layer of judgement on the action.