I assume you’re coming from a cake shop! 
I get what you mean, but you have kind of made my point for me though (possibly better than I did) – an enrichment of Scottish Culture and, I agree, probably a knock-on similar effect in the rest of the UK (though possibly more an assertion of Englishness, which may not be in the best interests of the Welsh and N. Irish, but that’s another problem) will naturally increase the individual nature of the two countries. Hence British culture as it is now *will* change, arguably for the worse *if* you’re coming from the point of view that the current mixing pot of culture is what you like and what you want to stick with with no changes. What it’s replaced with may well eventually be much better to most both in and outside of Scotland- this is a strange argument in that sense – but British identity will undeniably change and what we know it as will cease to exist. To use another cake analogy, you won’t get the same cake if you enrich one or two or more of the ingredients. It might be a better cake for the enrichment (I’ve eaten NIgella chocolate cakes with an obscene amount of stuff in, for example, and they’re great), but there’s no guarantees because no-one quite knows what the ingredients will be yet.
I think really what I’m saying is that I get where you’re coming from, but it’s possibly the wrong argument. Rather than saying British identity won’t change if Scotland leaves, which is untrue, it would be better to say British identity will change, but there’s a good chance that the new British culture that replaces it will be better, with stronger identities for the component parts. The trade-off being it *might* be worse overall or for some. That’s a risk, but I think an honest acceptance of it is probably the way forward.