I've always looked at it as bowling against another bowler, an average, doesn't matter if man, woman or child. Use handicap to make it more level and draw more bowlers or have scratch to let the skill prevail but probably fewer teams.
Years ago, while they still had the ABC Mens Open Championships and women were threatening to sue to be allowed to bowl in the men's only tournament, I had a discussion with a couple of good women bowlers. I asked why do you want to bowl in the mens tournament? More money to win in the mens tournament (more entries than the WIBC womens tournament). Well, if you are allowed to bowl in the mens tournament, will you quit bowling in the womens tournaments? No, that is almost guaranteed cashing (for them because of their higher skill level). How about letting men bowl in the womens tournament? That would be unfair because men are stronger than women. How about just letting lower average men bowl against the women, like 160 or lower? No, still unfair because men are stronger and they could sandbag.