I wouldn't be surprised if the death rates were lower right now. New York City had been the epicenter of the outbreak, and they had so many patients that the hospital system became overwhelmed, meaning people who might not have otherwise died were unable to receive treatment. Now that NYC has things much more under control, those who need hospital or ICU care are better able to receive that care and are less likely to die.
There may be another spike in death rates beginning quite soon as the hospital systems in Arizona and Texas become overwhelmed, owing to their aggressive reopening schedules.
Are we reaching herd-immunity levels and just not aware of it yet?
Not even close. Last I heard, herd immunity isn't a reliable protection until >90% of the (surviving) population has actual immunity. It's why small reductions in the measles vaccination rate led to some nasty outbreaks over the last few years. It's also why vaccines are generally preferred to letting a virus burn through a population.
(EDIT: Strange too how the media's focus has shifted from death rates to infections rates - since death rates at this point are no longer a sensational talking point).
ABC and NBC's nightly news broadcasts show the number of deaths and the chart showing deaths over time every night. They didn't stop, just because the death count was leveling off (well, relatively speaking--there's still 1k+ dying each day). I didn't think they were considered fringe media outlets.