I am just wondering, where and why are people taking 6 or more balls to bowl? If your bowling a PBA tourney or something with some tougher lane conditions, I can see needing 4 maybe 5 balls.. But IMO anything more that that is overkill, especially if your bowling on a house shot..
Is it just to show everyone how many balls you have??
For Sport shot tournaments, I'll usually bring my KR 6-Ball roller and a 2-ball Vise shoulder tot. Why? Because I want choice. In a strange house, you never know how a published Kegel or PBA pattern is really going to play. Having a choice between high and low RG equipment, drillings, and different surface preparations can be the difference between cashing and going home with your tail between your legs. I won the last two tournaments I entered because I brought the ball that otherwise would have stayed home.
Having lots of balls with you doesn't mean you're going to use all of them, or even most of them. It just means you have choice. And frankly, I could care less how it looks to anyone else. I'm there to compete -- not win a popularity contest. You're defeated before you start if you give your opponents that much control over your actions.
To the question of multiple 3-ball vs. 6-ball, it's a trade off. I have multiple Vise 3-ball rollers too, and I use one for taking balls to league. That's enough because it's a THS and I know pretty much what I'm going to face. But for storage, they do take up more room in the garage than I like.
In the end, there isn't a perfect answer between 2, 3, 4 and 6 ball carriers. It just depends on your particular needs.