[{"_id":"1","a":"b","b":"wanted value"},{"_id":"2","a":"c","c":"wanted value 2"}]

db.collection.aggregate([{"$addFields":{"arr":{"$objectToArray":"$$ROOT"}}},{"$addFields":{"v":{"$reduce":{"input":"$arr","initialValue":null,"in":{"$cond":{"if":{$eq:["$$this.k","a"]},"then":"$$this.v","else":"$$value"}}}}}},{"$addFields":{"result":{"$reduce":{"input":"$arr","initialValue":null,"in":{"$cond":{"if":{$eq:["$$this.k","$v"]},"then":"$$this.v","else":"$$value"}}}}}},{"$project":{arr:false,v:false}}])