You seem to believe that they would leave and/or not come the UK to work due to emotive drivers as pragmatically we pay extremely well in comparison to most parts of the EU and unless we bring in draconian checks the additional paperwork will be worth the effort of those seeking work. If there were any added.
If it is not an emotive and you few it as a pragmatic I don't think you're taking into account simple supply and demand factors on markets or the size of our economy in comparison to the rest of the EU.
I don't view it as emotive, except in so far as Britain will be viewed as less welcoming to other EU citizens if it votes to leave the community. And it would be viewed as such and if your implication is that people do not act emotively, you're greatly mistaken. But the larger part of what I said and which you skipped over are the pragmatic reasons. Right now, I as an EU citizen can apply for a job in any EU country, I can travel there without problem, I can accept a job without concern about any bureaucracy or rules stopping me or a sudden shift in government policy affecting quotas of foreign workers, etc. etc.
All of this vanishes if the UK leaves the EU. These are not non-issues. You are suggesting that they don't matter because of "supply and demand" or the size of our economy. They do. They make Britain less desirable than other similar countries for migrant workers. Even if a given migrant worker still comes here, it can be represented as an increased cost. We become a less desirable destination, ergo, we end up paying more on a national scale for migrant workers.
Furthermore, you're overlooking the fact that for the vast majority who will be voting "Leave" the issue they are deciding on is migration. Go into any workingman's pub and start a conversation about Brexit and count the seconds before you're talking about migration. You may protest that you have other reasons, but if Leave win, then it will because of migration and a desire to curb it (however mistaken they are about what leaving means). You cannot construct a reassuring argument that Britain would leave the EU and yet not make it harder for migrant workers to work here.
I mean, we could draw from other places - Africa, Pakistan and similar, but for European workers like Polish, Romanian... A Britain that is not in the EU immediately becomes less desirable as a working destination. There are emotive reasons for that, but primarily very clear practical ones.