The Happy SME-dium
Since too much focus on being a SME is bad and so is too little effort, obviously the answer falls somewhere in between. A happy medium is to introduce a greater separation of duties. In general, I find it is a bad idea to try to stifle a resource's request for knowledge and expertise. At the same time, it is good to reign in rogue resources who either unintentionally veer off course or secretly wish to perform a completely different job function from the one they've been assigned. One way to provide a greater separation of duties is to assign one or more resources whose sole job is to function as a SME in one or more areas. For example, have a resource who is solely responsible for being the AUT SME. The test manager is often best in this role, because he can answer questions relative to the overall system functionality in between all of the meetings that he has to go to. Another way to successfully provide separation of duties is to form an independent automated test team. This is an ideal solution, but teams often struggle in making that leap because they find it difficult to justify not having all of their testers actively testing new functionality. In complex environments, however, this move would be invaluable. Made up of one or more members, this automated test team's sole responsibility would be tool support or administration. All questions related to the development, configuration, and implementation of tools used for testing (including simulators, functional test tools, test management tools, terminal emulators, database tools, etc.) would be the responsibility of the automated test team. If everyone in the test group is interested in being a SME, perhaps the team can rotate resources in and out of the SME position.
Greater separation of duties ensures that no one is punished for attempting to gain greater knowledge and expertise, while still ensuring that each testing activity yields more effective results.