That's the moth, not the tree. Biston betularia is the Peppered Moth. Perhaps you should be more thorough. Mistakes that bad kinda make it look like you don't know what you're talking about.
Mutate and Survive
On two occasions I have been asked, – "Pray, Mr. Babbage, if you put into the machine wrong figures, will the right answers come out?" ... I am not able rightly to apprehend the kind of confusion of ideas that could provoke such a question. - Charles Babbage
Where we might believe that certain traits have been wiped of the face of the earth through "survival of the fittest", those attributes can live on, hidden and preserved, within the genome.
The operative word there being "can". Even then, I don't think that it can happen in quite the way that you're describing it. A recessive gene can't "hide" simply by dint of it being recessive. If two carriers of the recessive gene mate and produce offspring, it will be expressed. Given that this is a very likely occurrence, it would hardly be hidden.
But what if the allele is so strongly selected against that all of the individuals that carry it are wiped out? What protects against that? Nothing.
It is easy to picture such an example; if an allele that is adapted for water-rich environments is present in just such an environment, it would be beneficial. But if the local environment changed and became arid, that same allele could switch to being strongly deleterious. That could then lead to the allele being wiped out of the gene pool. Meanwhile, members of the same species that lacked that hydro-phile allele would survive. What protects against this? Nothing.
I am glad that we can "kind of" agree on this more modern definition of natural selection.
Actually, I think that you'll find widespread agreement on that one. "Survival of the fittest" was never more than a soundbite and in my opinion it gives a slightly misleading spin on things. "Survival of the best adapted" might be a slightly better way of putting it, or even "survival of the just good enough...".
Let's use your definition ie "survival of the just good enough". If the environment was so harsh that a particular trait could not even survive long enough to reproduce, then only individuals who are actively expressing that trait would disappear.
Sure. But it would still continue to be expressed. It's just that those individuals would be less successful. That is hardly "hidden", just less widespread.
It is possibly worth noting that there can be other reasons why a gene might not be expressed. Birds, for example, still carry the genes necessary to create teeth, but these genes are not expressed in the phenotype. It's nothing to do with dominance/recessiveness, but to do with developmental factors.
The unexpressed allele would still linger on in the population at large. These harsh conditions could even continue for thousands or millions of years. In every generation where the allele is expressed, the individual would die.
Well, not every individual, not necessarily. But yes, those individuals that expressed the poorly adapted allele would become markedly less common, or die out. That is natural selection. That's what natural selection is. Everything you've said here supports the standard evolutionary understanding of natural selection.
However, after enough time had passed, circumstances or the environment might change. Individuals who are now expressing the gene may actually survive or even flourish. The example that I am thinking of is the peppered moths.
Yes. It's a rather beautiful piece of evidence in favour of natural selection. Every single thing you've said here supports natural selection. Not that I have a problem with that; I just want you to understand that none of this is an objection to natural selection, indeed, it's quite the reverse.