Yeah, we have {basti} for that. With regards to the property {binxo}, an alternative is {co'arkai}, as well as {kaicfa}. Most useful though is plain {co'a}, either as cmavo or rafsi.
With regards to the original subject. The gismu definitions do have issues.
Some irregularities are probably oversights (e.g. {pluja} vs. {sampu}), others are a natural result of the non-systematic process of definition (see the occasional x3 in animal gismu). Some bloat does exist, which has an impact on the lujvo place structures, and some places are just too underspecified (see plini3 and plini4). Also see:
http://www.lojban.org/tiki/BPFK+Section:+gismu+IssuesNone of that I consider major issues, requiring a radical review of the existing language.
With regards to the proposal, fixed place structures completely miss the point of the generality of relations, which include, in addition to the mathematical ones already mentioned, spatial relations, family relations, grammatical relations, etc.
It is however valid to consider limiting the number of places, if not in the official gismu definitions, at least in usage. And if this is to affect the place structure of production lujvo, some agreement on which places are important will be necessary.