The distinction between federal action and actions by state or local government on this issue is important.
My understanding is that evictions are ordinarily almost entirely a matter of state and local law. As just one example, here's a description of the eviction process in California - https://www.courts.ca.gov/27701.htm .
State and local governments can put a moratorium on evictions or otherwise delay evictions, and many did so earlier this year - https://www.nolo.com/legal-encyclopedia/emergency-bans-on-evictions-and-other-tenant-protections-related-to-coronavirus.html .
Beyond the principle of remaining consistent with historical division of responsibility between federal and state governments, there is also the reality that economic conditions vary considerably from state to state. As of July, reported state unemployment rates ranged from a low of 4.5% in Utah to a high of 16.1% in Massachusetts ( https://www.bls.gov/web/laus/laumstrk.htm ). Emergency government action regarding evictions that makes sense, on balance, in Massachusetts may be poor policy in Utah. It's therefore reasonable to leave this decision with state and local governments, which have the power to take actions (or not) in response to their differing situations.
Have any countries with estimated cumulative infection rates similar to the U.S. experienced second waves where fatality totals approached earlier peaks?
Going by information at the Worldometer site, for example, Spain, France, and the UK have experienced cumulative reported per capita COVID deaths ranging from about 25% lower than the U.S. level (in France) to about 6% higher. I take that as evidence that the cumulative level of COVID infections in each of those countries is broadly similar to the U.S. In each of those 3 countries, the 7-day average of reported daily COVID deaths during a recent second wave has - at least so far - stayed below 20% of peak levels in the spring.