Yes and no. They usually mark the end of a war. The last was in 1991 after Desert Storm. Inaugurations also include a large contingent of military. There have also been large ceremonies, attended by Presidents, that mark special anniversaries - the annual anniversary of D-Day in Europe, or the 50th Anniversary of VJ day in Hawaii in 1995. All of these include some form of military parade, inspection, or other activity.

Smaller parades and inspections of troops involving the President usually occur with visiting heads of state (this is what the Old Guard in DC exists for) as well as other ceremonial activities and visits to troops overseas. The President is the Commander in Chief, and there are prescribed ceremonies fo him and a host of other dignatories and senior muckety-mucks. In fact, the number of guns fired in salute varies according to who they are firing it for. For example the President or a head of state gets 21 guns, but the VP only rates 19 and a Counsel General or a Division level officer of a military gets 9.

To my knowledge the request from President Trump did not specify Memorial Day, and that would be a particularly bad day to hold a triumphant parade, and one discouraged by the Pentagon and Veterans groups. There are three holidays that are associated with the military in the US and they are often confused:

Memorial Day - a day to remember those who died in war.

Veterans Day - a day to honor veterans (also this is Armistice Day, which marks the end of WWI).

Armed Forces Day - A day to honor those on active service.

A military parade would be appropriate on Armed Forces Day (or the Fourth of July). One could also hold one on Veterans day, especially this year, as it marks the 100th anniversary of the end of WWI.

Memorial Day is not a day for parades and is usually marked by solemn ceremonies at National Cemeteries across the United States and cemeteries maintained by the ABMC around the world. The ABMC ceremonies are very moving, as most of the attendees are usually local groups in places like France, Belgium, and Italy who honor the US war dead as liberators. Memorial Day is also the day the President will typically visit Arlington National Cemetery and lay a wreath at the Tomb of the Unknowns.

While big parades like the one President Trump attended in France, or the ones we associate with places like North Korea, are rarer in the United States, they are not unheard of. The media, eager for Trump headlines, may be playing this up to be more than it is. For example, the idea of a parade to mark 100 years since the end of WWI is not a bad one and one that the WWI centennial commission in the US might actually welcome as it has not been hugely successful in generating the widespread interest in WWI commentation that one sees in Europe, though it has a number of events in the works (and has accomplished a few already). The dedication of the new National WWI memorial at Pershing Square in Washington, DC would be a good opportunity, for example, if they ever get around to finishing it.