I'm not sure what you mean by a laughing stock. Please explain. In health care professions, for example, non-compete clauses are used to prevent doctors from opening up next door and taking a clinics patients with them. There is not physical product involved in such a case either. But a definite money issue exists. This also occurs with other skilled employees (I used to work in human resources).
I agree it may be difficult if teachers are not on the payroll and are paying dues. However, unless uchideshi a higher ranked instructor is likely donating teaching time and could cause serious financial harm to the school should he leave and pull loyal students. Students should have the right to go where they want to, however, in the role of a head instructor students could be guided to the instructor through one on one or other means (they probably have access to addresses, etc.). Taking students would be taking business although this is not something that could be trademarked or patented (aikido is aikido). Perhaps a lawyer could respond to this one.