Many on the leave side would (and did) say that while the EU/EEA has succeeded in lowering some barriers to trade between EEA states, it has at the same time (1

Many on the leave side would (and did) say that while the EU/EEA has succeeded in lowering some barriers to trade between EEA states, it has at the same time (1) raised new barriers to internal trade within some EEA states and (2) maintained or raised new barriers to trade between EEA states and states outside the EEA. This is particularly stark when new member states have acceded and as a result new tariff barriers put in place, as was the case when the UK joined the then EEC (this caused significant damage to the UK's relationship with New Zealand, for example). But it's also true in the way that the EU/EEA views product regulations and standards, which (many would contend) have a protectionist effect. One example commonly cited in this regard is REACH. Many leave campaigners expressed a desire to deregulate in these areas in order to lower barriers to trade in ways that were not possible within the EU/EEA, as well as to lower tariffs unilaterally post-Brexit. I don't think it's fair therefore to say that Brexit damages "lower barriers to trade" - it really depends on what kind of Brexit there is whether that's true or not.