It depends on where your coming from doesn't it? A carefully planted bed (and not sprayed into oblivion) with a mixture of natives and non-natives from similar climates offers good diversity and a long season for pollinators - that's if it's not full of double petalled flowers which don't produce pollen and have little to offer. Some invertebrates are specific in their feeding, and non-natives won't attract them, others like spiders are interested in the infrastructure and don't care whether they dangle their web from a native or a non-native, or even garden furniture or a basket that's been left outside too long.
A carefully tended "weed free" lawn has very little to offer wildlife.
A "wildflower" area is probably as good as the flower bed in the summer but doesn't give as long a season (though a quick look at the number of caterpillars whose food plant is some type of grass gives the lie to it "only" producing hay). And since most people turn either lawn or just one bed to wildflowers it's going to be an improvement. We're not talking in general about people turning over their whole garden to a hay meadow.
The RHS research and advice makes it clear that "near natives" have a valuable contribution to make.
Something not to be overlooked is that the "rewilding trend" has brought a lot of people into an interest in gardening and/or nature conservation and this is of more value than any individual contribution. No government will deal with climate change in an effective manner unless they think there's votes in it.