I assure you that there is nothing in the ADA that requires a company to take on liability for items patrons want to drop-off for collection by third parties later. As a matter of fact, the ADA only requires accommodation allowing patrons to use mobility devices; ADA does not require a public accommodation to facilitate acquiring a mobility device.
The last time we needed an ECV for my sister-in-law, we were there to collect it from the company as they arrived to drop it off and were there to meet them to have them collect it when our trip was done. Back then, of course, no one held the kind of excessive entitlement that pretends to rationalize your complaint. Back then it was just the normal thing to do at Disney - and it is precisely what she does at every other vacation destination they visit today.
And this is a really important point: The problem here actually is the exploitative third-party suppliers who are not willing to provide the level of service that their patrons need, i.e., drop off and pick up on the patron's schedule rather than whenever it is convenient for the third-party supplier. They're just aiming to skim off the cream while trying to shift reasonable costs of their business on to someone else.
