Symptoms: all threads in BackgroundScheduledPool busy, lot of tasks in replication queue, none of the tasks is executing. 

![Screenshot from 2021-04-16 16-21-44_](https://user-images.githubusercontent.com/1549571/115193796-e767d600-a0ec-11eb-887c-5c9c2412e50c.png)

Related to #16895

Possible workarounds (poor options): increasing the background_schedule_pool_size to huge values, or restart server every time when that happens etc. - 

const DataPartPtr & part, Coordination::Requests & ops, String part_name, NameSet * absent_replicas_paths)
{
    if (part_name.empty())
        part_name = part->name;
    auto local_part_header = ReplicatedMergeTreePartHeader::fromColumnsAndChecksums(
        part->getColumns(), part->checksums);
    Strings replicas = zookeeper->getChildren(fs::path(zookeeper_path) / "replicas");
    std::shuffle(replicas.begin(), replicas.end(), thread_local_rng);
    bool has_been_already_added = false;
    for (const String & replica : replicas)
    {
        String current_part_path = fs::path(zookeeper_path) / "replicas" / replica / "parts" / part_name;
        String part_zk_str;
        if (!zookeeper->tryGet(current_part_path, part_zk_str))
        {
            if (absent_replicas_paths)
                absent_replicas_paths->emplace(current_part_path);
            continue;
        }
        ReplicatedMergeTreePartHeader replica_part_header;
        if (!part_zk_str.empty())
            replica_part_header = ReplicatedMergeTreePartHeader::fromString(part_zk_str);
        else
        {