SolrCore.logid is used mostly by some log statements within SolrCore to log the core name at the start of some (not all) log messages. It pre-dated MDC and I believe it's basically obsolete now, and contributes to needless logging verbosity. The info levels where this appears if for opening a new SolrCore, closing a SolrCore, registering a new searcher, and it's in the "requestLog" and thus will show up once for any HTTP request into a core (e.g. select, update, etc.). So removing this will disturb anyone parsing Solr's logs. Maybe this should wait till 9.0?
There is some value still because for cross-core join query, any pertinent log statements on the "fromIndex" would ideally be reported against that core and not the toIndex. That seems too minor to keep this old stuff around for though.