One of the interesting aspects of immigration is shortages of labour. As far as I remember, they have always occurred, and often in the same industries, e.g. catering, agriculture, health, skilled trades. The EU provided a quick solution - if there is a shortage of lorry drivers, bring in some Polish ones.
One reply to this is that we should train our own lorry drivers. Yes, that's fine, but then the shortages may crop up in another industry, so do we start training for that? Some people say, use the unemployed, but of course, they need to be trained as well.
This relates to the issue of 'control', since we don't control shortages of labour, and immigration is often a response to them. The risk is that denying immigration, clogs up the supply of work.