I don't think it's impossible to have both. In the simplest sense, just look at the PBA tour. Most all of them are what we consider tweeners or up. People call Walter Ray a pure stroker, but he isn't even comparable to the same league bowler we call a stroker. He throws with good speed, and I doubt he has a problem throwing 300rpm, a "tweener" ball, while we name Joe Stroker the same term, though he throws it 14mph with 200rpm. And like I said, WRW is considered a stroker on tour, meaning that the others all have more "power". And obviously they are all accurate.
I think the problem stems from the fact that everyone associates being accurate meaning you're WRW or Parker Bohn, when realistically all players on Tour are accurate. Same with power. Guys like Mike Machuga, Chris Barnes, etc aren't considered massive power players, even though compared to your average league bowler they have far more (effortless) power. It's really a matter of semantics.
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- Andy