Hygiene, nutrition and medicine (all good things!) also cause us to remain alive where previously natural selection would not have favoured those bearing too great a mutational load.
I doubt that existing mutations have been fully 'tested'. We know that the majority of mutations are harmful and that the brain is far from fully-developed prior to birth, for instance. Being complex there are many genes which control its development and it seems plausible that the result could be sub-optimal without obvious signs of disease or disability. Other things being equal, we could be slower, less resilient, less fertile, etc, than our 18th century forebears.
I do see the argument you are espousing but I would only suggest that you consider the broader context of what happens when new species arise. I suspect you care more about the elimination of alleles (which is surprisingly hard to do), but this is a good example for why I disagree:
One possibility for speciation is the creation of a new niche (lets say a new type of tree grows on an island, its seeds having been carried there by an unusual current). Here, organisms might have increased reproductive opportunities over their neighbors by exploiting this new tree. In time, one could imagine organisms that live in the new tree, like microbes, could acquire enough new features to constitute a new species.
Consider the case where organisms from the original population become unable to grow on the new tree. If the new species is also unable to grow in the original environment, how can we say either is more or less resilient?
(1) humans have universal intelligence which gives us the ability to adapt to any environment, (2) human evolution is now swamped by the evolution of memes, not genes. We now decide what to do (including whether to speciate or not)
A more realistic analogy from the animal kingdom would be something like the case of farmed salmon which within a very few generations are less healthy than wild salmon. Also the famous 'mouse utopia' experiment. Both situations where the environment has been artificially manipulated by (human) ideas, just as our present environment is. Mutational loading is one explanation for the results.
So have you considered the issue of mutational load: what's the greatest load we can sustain and what's its present level? Is it responsible, for example, for the declining birth rates in the West or is the explanation for that purely sociological?
I would like to know the answers. However I presume that we'll start by using CRISPR or similar tech to eliminate known genetic diseases like Huntington's and Tay-Sachs. From that precedent should follow the identification and elimination of new and more silent genetic abnormalities. Which is reassuring.
But to your example, one issue with the farmed fish is that they now constitute a closed gene pool - we can easily explain their decreased fitness with the likely rise of harmful alleles.
With the explosion of population, I don't see much relationship between the salmon and humans.
This seems like a reasonably accessible (college-biology level) discussion of what evolution would look like in the human gene pool:
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2933187/
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EDIT:
I suspect you'll need a university library to access this, but Dr. Pardis Sabeti is well known in this area and also an amazing person - she played a big role in the molecular biology work that underlay the US response to the Ebola crisis. She wrote a review that explains the tools we currently have to ascertain human evolution:
I go for dumber people helping each other to live happy, fulfilled lives over intelligent super people destroying one another so they can control the most resources.
The problem though is that happy dumb people will have an even harder time competing for scarce resources against genetically engineered unemphatic super geniuses than they do against the current crop of sociopaths that run the global economy.
Also, to support your claim, one would need evidence that the child mortality of the past reflected genetic unfitness (as opposed to poverty or the unavailability of antibiotics).
In any case, we have to go back to the question that the GP asked, that dogs are malleable doesn't help us. Does reduced child mortality really cause more mutations to accumulate?
However, dog breeds are not species and, given their non-random mating, don't really tell us much about whether 200 years is long in vertebrate evolutionary time.
As far as humans go, I will grant that allele frequencies may have changed if you pick an isolated subpopulation of humans (say, everyone in Greenland) but even that seems extremely unlikely.
As an aside, there are researchers who are using the caste system in India as a way to explore genetic architectures within a civilization. As these castes have existed for considerably longer than the period we're discussing, meaningful allele frequency changes may arise.
http://wasdarwinwrong.com/korthof97.htm
I would guess it is wrong; we are on a track where genetic manipulation to treat blatant defects will (relatively shortly) be cheaper than the traditional medical treatments.
Parents could choose to have children created from their healthiest genes, rather than leaving children to be shotgunned with a random and increasing fraction of damaged genes. Genetic repair would replace the ancient cruelty of natural selection, which only fights entropy by tormenting organisms because of their genes.
The concern espoused above is that we won't be able to fix the problem.
Now that's a limited view of the process that created life. Natural evolution also pays back by upgrading the gene pool.