Er, the Leave campaign was expressly against free travel, and it's kind of silly to think you'd get the same trade terms leaving the EU. So the choice you provide to support the idea that maybe the leavers have it right is neither one the leavers are offering (on the travel part) nor one that is remotely realistic on either point as a result of voting leave (it's something that might have been achievable by staying in and advocating a different course for the EU.)

And you live within a representative, rather than direct, democracy which features non-binding referenda; the people speak with binding authority through elections of representatives. There may be reasons that the government should put the results of the referendum into policy, but appeals to the nature of the system of government do not provide that reason.