Captive shops can be big on getting new agents to take out policies on themselves in the name of "believing in what your selling" to help you sell.
MLM companies do likewise.
How can you sell Amway soap unless you use it yourself? The "personal testimony" pitch.
Doesn't make much sense when talking about life insurance. You can't prove it works as long as you are alive and very difficult to make your weekly quota when you are dead.
There are plenty of agents selling Medicare plans that are 30 years away from Medicare eligibility. Some will talk about selling the same plan (or something similar) to their parents or grandparents. I suppose that helps close the sale but I doubt it.
If owning what you sell gives you more confidence then go for it. But as Bevo pointed out, if your prospect does not trust you it really doesn't matter how many policies you own because you are not going to make the sale.