In most league settings, you can get by on a limited amount of equipment. Bowling league and having handicap are very different from tournament bowling where you score bad, you go home.
If I am leaving a few tenpins during league, I usually won't change balls, especially if I am using one that fits my hand really well. I will do as you suggest and make adjustments with emphasis on making as good a shot as possible. Then, if it doesn't carry, I may fiddle around with another ball, but I may not either. My leagues are for practice of repetition and fun anyway.
If I get into a tournament where carry is everything, I will attempt to match up with the ball that gives me the pocket most consistently and still carry with a good ratio. Sometimes nothing I have is any better than the others, but at times, one ball will ride head and sholders over the others and I am VERY hard to beat because I have a matchup that the other bowlers may not have available to them. Having several balls to choose from only means that you are increasing your odds of having a ball that will "match up" well, especially if you have a wider variety of equipment ( i.e. pearls, solids, particles all drilled in deifferent configurations )
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