Bottom line on the sovereignty point is that laws made specifically to suit the UK will always be better suited to the UK than laws designed to take unto account 27/28 different countries with lots of different priorities. Sure there were a lot of laws that were specifically national competencies when we were an EU member but there were also a lot that were not. And the EU is gradually centralisimg more more more of these powers - that is what it does. I don't want that, same as plenty of other people judging by the referendum result.
On the immigration point, you're right that we gave up the ability to return illegals to France, but as is pointed out on here, the numbers of illegals are a lot less than the number of legal migrants from the EU, who we had no choice but to accept when in the EU. Sure, we need to deal with immigration better now but we have the choice.
In any event, regardless of the above we are out and there is no reasonable prospect of rejoining. Probably for the best given the EU seems determined to tax and regulate itself into relative economic irrelevance. Below is a graph showing EU GDP as a percentage of global GDP. Put bluntly, who wants to hang around with losers?
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