No, you should not add master-eligible nodes to solve a problem related to a lack of coordinating nodes. Instead, you should add coordinating nodes.
These docs recommend against using master-eligible nodes for coordinating client traffic:
While master nodes can also behave as coordinating nodes and route search and indexing requests from clients to data nodes, it is better not to use dedicated master nodes for this purpose.
These docs give advice on how many master-eligible nodes to have in your cluster:
However, it is good practice to limit the number of master-eligible nodes in the cluster to three. Master nodes do not scale like other node types since the cluster always elects just one of them as the master of the cluster. If there are too many master-eligible nodes then master elections may take a longer time to complete. In larger clusters, we recommend you configure some of your nodes as dedicated master-eligible nodes and avoid sending any client requests to these dedicated nodes. Your cluster may become unstable if the master-eligible nodes are overwhelmed with unnecessary extra work that could be handled by one of the other nodes.