So this card is actually not bad in true solo. It is expensive, yes, but the unlimited heals on it can really be helpful at times. You can always make use of the doom heal during witching hour turns. Agnes can get some good use out of this, but so can any low health mystic.
There are some neat synergies with the new cards in TSK as well. Amina can use Word of Woe to get herself some extra healing without using an action (and also possibly clear the doom by healing the last point with her next action); Sin-Eater can also get extra healing juice as well, if you really need it (and in true solo, sometimes you do).
Amina can also pay for it easily too, either with her ability, or even with Sleuth, which may see new life in Amina decks. The chalice is also not a bad pick to slot in with the new Astral Mirror.
Obviously, one must be wary of the agenda clock when using the chalice, but that's the cost for dealing with doom!