The border checks would be no different than it is for people from norway or switzerland, still it would be worth it and iam sure that these people are aware of the affect that leaving the EU would have.
I can see that you aren't too clued up on EU politics.
The EU have made it very clear to the UK in the past that if they leave the EU, there won't be any favours along the type given to the EEA countries and Switzerland. It's just not an option on the table to leave the EU and still retain all the benefits of membership.
Norway (and the other EEA countries) pay quite a bit each year to the EU as well, without having a say. Take the Schengen treaty - Norway and Iceland were facing immigration checks into the Nordic countries, to which they had historically no frontier controls. Schengen was effectively forced on them through the carrot and stick approach - and now, if the EU decides to change something about Schengen, Norway and Iceland don't have a voice.
Switzerland also had to agree to quite a lot to maintain their position - the most notable one is Schengen, but they had to agree to quite a few things, such as the freedom of movement of EU nationals in Switzerland (and the right to live and work there) in order to maintain the benefits that they get, such as no tarriffs on their goods.
The EU made it very, very clear to Switzerland that unless they agreed to implement a huge chunk of EU legislations and treaties, then every agreement would be torn up and Switzerland would become like Ukraine or Russia to the EU. The same would happen with the UK.
Do you seriously believe that the EU will want to keep giving UK nationals ease of access
As for our Irish member - do you want a return to pre-1993 when you could only cross the Irish border at certain approved crossings and be subject to Customs controls whenever you cross? Thought not...