This is a great question. I think technology is certainly changing the kinds of selection pressures humans face, but arguably it always has done that (for example, access to fire or another new kind of tool or knowledge about a novel food source has provided advantages for longer than humans have existed as Homo sapiens). I think there are a few factors important to evolutionary theory at play here.

First, genetic drift is arguably a stronger force than natural selection in evolution anyway. This was a major point of debate in the development of modern evolutionary theory (see the work of Motoo Kimura). That is, chance events, e.g. everyone in an area being wiped out due to natural disaster leading to loss of some unique genes that may have been very advantageous, can actually have a much greater impact on gene frequencies than selection on one particular trait out of many. In particular, a gene is much more likely to go to fixation (that is, spread to every member of the population) if most of the population dies in a "bottleneck" event. If this is the case, then the "rate" of evolution won't be much affected even if selection pressure is lessened. This is particularly important for your argument about beneficial mutations failing to spread: it's very rare for a beneficial allele to reach fixation driven by positive selection alone. Since this type of event is exceedingly rare in nature, it's hard to know whether we can reduce it with technology and society. However, your argument is about natural selection, so I will address that primarily from the perspective of "purifying selection" (loss of harmful alleles) here on.

I see three possible counterarguments. First, access to the kind of expensive, high-tech medical care you're talking about is not evenly distributed across the world's population (e.g. people living in rural India vs. Manhattan have access to different treatments, as do Bill Gates and I to some extent). Meanwhile, the population of humans is very large right now compared to all past times, and is getting much larger, and also more able to come in contact with one another because of transportation innovations. So, it might be possible that "natural selection" per se will end if we make it to some utopian, Star Trek kind of future, but for now we have a very large population with only a very small percentage of it able to access advanced, life-saving medical care for heritable conditions. As others have pointed out, we may edit these deleterious genes out of our population in the future.

Furthermore, besides genetic diseases, we are in a constant arms race with bacteria, viruses, parasites, and other nasties that can kill us. Lots of people of European descent are resistant to the Black Plague because their ancestors survived a bottleneck (everyone who couldn't survive the Plague died); lots of people of Sub-Saharan African descent are resistant to malaria; and it turns out a good number of people are resistant to HIV. Because those diseases are always evolving, they may be hard to keep up with even in an era of advanced medical science.

However, I would argue that even in a world where all or most people have equal access to healthcare, making genetic diseases irrelevant to selection, other selection pressures remain. For example, driving a car is objectively dangerous, and someone prone to distraction or risk-taking is more likely to get into an accident. It's not just car accidents, and the personality reverse is also true: people with anxiety disorders have lower rates of accidental death, presumably because they are less comfortable with risks like driving fast, handling firearms, extreme sports, etc. or possibly because they just don't feel like leaving the house (: I use this example because many people would not immediately think anxiety is an adaptive trait. It seems likely that we have more adaptively significant traits that are not so obvious.