Authorities have not commented on a possible motive. A 33-year-old man with a history of mental illness has been detained in a secure psychiatric hospital on suspicion of arson.
Others want a partial or complete rebuild. They are wary of the risk that an untouched ruin could become a site of neo-Nazi pilgrimage, at a time when Germany is seeing a resurgence of the far right.
No decision has settled the argument. The choice still runs between rebuilding in part or in full, and leaving the site to nature so that its Nazi past is forgotten.
The blaze has revived a familiar argument over Nazi-era places: whether to preserve them, alter them, or let them disappear.
Some want the building abandoned, the ground returned to nature, and the memory of its Nazi past forgotten.
The house stood on the Obersalzberg at 1,834 metres (6,017 feet) above sea level, overlooking the Alps. Visitors could eat sausages in a beer garden there.
Blume does not believe"a one-on-one reconstruction"of the site is possible. On Bavarian radio, he made clear that"it should not and must not cost the taxpayer anything". Police said the Eagle's Nest itself was"largely destroyed". A documentation centre on the site survived unscathed. One critic said the Kehlsteinhaus was just"a Nazi vanity project"since romanticised by the name Eagle's Nest.