I am not sure that a federal agency can control a public company's profits (except maybe a utility or monopoly) but they can put consumer protection regulations in place that can effect the business model.
Imagine a regulation that would require a timeshare company to buy back properties at a certain percentage of the current RETAILsales price. What would happen if the rule is that Jane buys a week for $20,000 and then timeshare company is required to buy it back within a five year period for 50% of the selling price at the time?
Or rules put in place requiring timeshare companies to eliminate restrictions on resales. Any benefits, programs, etc. associate with a week or unit or point must carry over to the new owner.
I don't think the problem is the profit margins - plenty of industries make a lot of money. The consumer protection required is how the product is sold, resold and the right of the consumer to terminate the relationship.
I am happy to be a timeshare owner but if I was told at the sales presentation that it would be for life, regardless of my job, health or income status, I would probably never have bought and can't imagine anyone buying.