How could you mine underneath it without drowning? Even if you could it would 99% stay in place just like several other 'permanent items. Rune stones, troll caves, etc.
I was wanting to build under the Elder altar but the first one I found was just sitting on the water table like yours. I searched around for some time for another and found one that worked out well.

https://steamcommunity.com/sharedfiles/filedetails/?id=2811747084

https://steamcommunity.com/sharedfiles/filedetails/?id=2810249936