Lion-tailed macaques are not being phased out on purpose, they are dying out because the population is post-reproductive. The herpesvirus that lion-tailed macaques carry is not "a major problem", it is endemic and generally benign in several species of Old World macaques. It is very dangerous to humans if contracted, but the few instances of this occurring have been in research labs; zoos can and do mitigate the risk through proper barriers and sanitation protocols. However, a combination of fear about the herpesvirus and changes to exhibit planning in previous decades led to a slowdown in breeding that caused a total collapse in the population's reproductive capacity; that is why they are post-reproductive now, not because of a conscious top-down decision.
The vast majority of species that are phased out were not viable to begin with. Very few species are phased in because there is limited space for them and because it requires individual zoos to expend resources acquiring them and gaining husbandry experience. In any case - as is stated often on this site - you can prioritize conservation in ways that doesn't involve replacing common species with endangered ones.
Not when the Japanese Macaque is the only macaque species that is widespread on the continent, has a healthy breeding population, and is uniquely suited to cold-weather zoos.
Very few (if any) AZA zoos in the southern half of the US keep Japanese Macaque; most of them don't keep any species of macaque nowadays.
Because there are aren't any oncillas to replace the ocelots with
As a general rule, the answer to "Why do American zoos keep the more common _ instead of the rarer _?" is "because that's what they already have." Generally speaking, species that are already well-established in American zoos are prioritized for management, species that aren't viable or aren't in American zoos are not. This is all on a case-by-case basis; a lot of factors go into choosing what species to work with, it is not just a matter of which one is more threatened (although that is one factor taken into account).
This is an area where I too wonder if there is something for them to re-evaluate. The membership dues can be a burden on smaller facilities, and some of the newer standards - such as being required to have a full-time veterinarian - are not financially feasible for some facilities and may not be necessary to maintain proper animal care. I've also noticed that in recent years smaller zoos have been denied re-accreditation based on "outdated enclosures", despite larger zoos with very similar types of enclosures being re-accredited without issue. I'm not sure if this is bias or genuine differences I don't know about, but I find it a concerning trend.