On the surface, this seems like a worthwhile objective. The bookkeeping is simpler than NAIC's recommended Valuation Unit system, and everyone has an equal say in the operation of the club. There are, however, some drawbacks that may not be evident at first, but which become serious as the club matures.
Some members pay late.
If you use Valuation Units, the number of units purchased depends on the value of a unit at the time the payment is received. If a member pays late, and your portfolio's valuation has increased since the last meeting, that money will buy fewer units than money invested on time at the previous meeting. Financial emergencies do occur. It can't be done. Some members want to increase the monthly payment.