Is it profitable and if so how?
From what I understand they earn 20% commission from bookings made, but what is the CAC of that customer? And what of their LTV? At the most wouldn't they book a holiday twice a year?
Please explain how these type of businesses can ever be profitable because they're not hiking the prices but selling on commission.
HH is profitable because they're dealing exclusively in the luxury market where there is enough room to earn significant commissions and none of the booked experiences are low-dollar. Along with the luxury prices is the luxury expectation, where there aren't many self-bookers.
Remember that there used to be a lot of travel agents for all levels of travel and self-booking was a rarity. Now you mostly see travel agents who book bundled experience travel, not simply hotels or flights. Your ability to profit in travel has to do with your ability to drive value. Is it too easy for a consumer to make the same arrangements themselves?
As for CAC and LTV, this is where you will need to validate your own marketing strategy. There's historical data on the travel agency business, but that business died out and was re-invented. It doesn't mean you can't learn from the old models though.
Consider why customers use agents. That's where you start. Make a list of your assumptions and test each one. Validating your marketing strategy here is no different than for any other business, and it is always the first step before deciding whether you even have a sustainable business.
Luxury/niche buyers do not have the same buying patterns that you see in the general public. Twice a year holidays are not a limit. Getting value is an absolute demand though.