Why won't HVAC supply stores sell directly to the public?
Their insurance may lean that way. Rates are probably lower if they are not selling to end-users. They may also not have to deal with sales tax, if they are not selling to end-users.

As for the (or more) economic incentive many take for granted: the cost of customer service. The below consumes valuable man-hours and to staff this could double payroll:

They may also prefer dealing with competent licensed professionals, because they will have less time wasted on "dumb questions" (there are such things, really, even if you've been told otherwise) and irate "genusies" who bought the wrong thing for the wrong job and want a refund because it didn't work, or because they are used to getting "free rentals" by exploiting big-box-store policies that allow them to return things even after they have used them.

The competent licensed professional also provides them with a repeat/regular customer base - how often do YOU buy an air conditioning system? How many do you buy per year? Do you buy parts by the case? Less of their time spent moving more product is more profit for them, even if they sell it at a discount to the professionals (which is common, based on volume.)

There is also a concern about the proper handling and recycling of refrigerants - few if any homeowners own a vacuum pump, much less a refrigerant recovery system.

There are websites that sell various things (I happen to have been looking at mini-split system heat pumps recently) but you still need a licensed installer to assemble them; both for legal reasons (EPA) and practical ones (that vacuum pump, etc.) In many cases, you'll do better to just buy the system from a local installer than to buy it online and then pay an installer to assemble it for you.