If you're talking in terms of large numbers of consumers (e.g. a political solution), it's better to shift the dietary plan in the direction you suggest. But the more an individual human consumer minimizes red meat, eggs, and dairy in favor of plant foods (assuming that the plant foods are sustainably grown), the further the individual moves the needle toward planetary health.
There are three possible reasons for choosing an entirely plant-based diet: reducing environmental damage to the planet; maximizing one's personal health / well-being; reducing / eliminating cruelty toward sentient beings. The personal health rationale is (according to current scientific research) flexible and debatable. The third reason (reducing / elminating cruelty toward sentient beings) is fairly straightforward.
Your analysis focuses on environmental / global well-being. If this is the primary reason, then one's goal must take into account how the plant and non-plant (eggs / red meat / poultry / dairy sources) sources are raised. In general (and this is a generalization), factory farming of plant and non-plant sources can be quite detrimental to the planet's health. But if the consumer isn't willing or able to factor in all the variables, then this simple approach / design may be helpful: In terms of planetary health, it's more beneficial for a human consumer to eat a meal of soybeans (or corn or wheat or a combo) than to feed soybeans (or corn or wheat or a combo) to an animal and then harvest that animal for food.
Summary of plant vs. combined diet benefits (there are no benefits that I'm aware of for an entirely canrivore diet for humans):
(1) minimizing damage to the planet. Entirely plant based: more beneficial than combined, though the sustainability / availability / practicality of each source must be taken into account.
(2) reducing cruelty to sentient beings. Entirely plant based diet is a clear winner.
(3) personal health / well-being: no clear winner. Observational data that I'm aware of indicate that a mixed diet (that favors fish over meat and dairy, and plants over fish / meats / dairy) in general may be the healthiest option, but it's possible (though difficult and relatively expensive) to create an entirely plant-based diet that rivals the benefits of the mixed diet.
Most people make a political decision every few years. But we make individual dietary decisions each time we sit down to eat.
