For clarification, there are no pre-built lists in Member Tools. You must make your own lists and you must manage your own lists. It doesn't have the options that LCR has to let you send a message to, for example, "Ward Council" without first manually setting up a list of ward council members in Member Tools. I think you will probably have to manually adjust the list when changes occur, but cannot verify that - I have never gone to the trouble to set up a manual list on Member tools.
While many have reported recent issues with the Send A Message tool, I have not had any issues using it. I have had a few undelivered but those appear to be valid (member likely changed their email address or their email address was edited by our ward clerk to prevent delivery of the message because they had requested no contact). It may be broken in some specific cases or regions, but I don't believe it is broken for everyone everywhere. I have my own personal opinions about possible reasons (I'm not in an IT field so they are just guesses), but my opinions on this are unpopular with some who claim this is a church problem that they don't care to fix so I'm now just keeping those opinions to myself.