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Responsible pet owners already prevent cats from eating birds. Dozens of songbird species have gone extinct because of people who let their housecats go outside without supervision... it's not "natural" in any sense to artificially sustain a predator animal so that it can periodically go out and eat songbirds. If housecats had to sustain themselves on what they could catch, there would be much fewer of them and the sustained effect on bird populations would be much smaller.