@mightymoe I'd say that almost all of us survey for our clients, and if we are burying the monuments, it is for the client's safety or to ensure that the primary physical product of our work is remain durable and useful for as long as possible.?ÿ When buried, it's not hidden from the landowners if they are made aware of its presence when set.?ÿ They know where it is and can even dig it up themselves if they need to.?ÿ But I'm not leaving a tripping hazard for them, which also becomes their liability the moment I leave if one of their guests, landscapers, or in some jurisdictions, even trespassers trip and hurt themselves on it.?ÿ It is also far less likely to be disturbed by a mower or other equipment, or to get moved or removed by a disgruntled neighbor in the event of a dispute.
Your examples of the Washington and Lincoln memorials doesn't fit.?ÿ Completely different kind of monument.?ÿ They don't mark boundaries but commemorate history.?ÿ Their sole purpose is to be visited and displayed.?ÿ They are also not easily moved and are so obvious as to not present tripping hazards to anyone paying even mild attention to where they're going.
But if you want to start going far afield in discussing monuments, another type of monument is a time capsule.?ÿ They are most often buried or otherwise placed in a location where they are not readily visible with the intent that they will be unearthed at some future date to be viewed/used.
I've never seen in any survey text or read in any boundary case that a boundary monument was any less valid simply because it had dirt on top of it, but have read a few where a surveyor was criticized for not digging into the ground to look for one.