The reason why France and Germany in particular wanted to join the Steel Union as it then was, was to bind themselves so closely with France on an economic level that another European War would be unfeasible. At the time De Gaulle stood against Britain, and Churchill was particularly keen to be in from the start. I think Europe would be quite a different place, politically, if we had not been vetoed in the early days by the French administration.
The reasons why the Eastern European countries wanted to join does vary by the individual state. In many ways Poland and Czechoslovakia [as it then was] are part of the middle European culture that Germany in particular is the centre of.
As for the other Eastern European countries, they were on the rebound from Communistic Dictatorships [as were Poland and Czecho, of course] and they would do anything more or less to add security for their exposed position in relation to Russia.
I find it interesting that as soon as Germany re-unified, Norway [the voters not the politicians] decided that joining would not be a good idea. Earlier Norway would have joined, but things were left too late by politicians in the EEC and in Norway.
On the whole I suspect Poland would be somewhat dismayed in the UK votes to leave Europe, and certainly the Irish Republic is not happy either. But which ever way the vote goes, the planet will continue to revolve about its axis, and trade will continue, and it will not result in Russian invasion.
A good settlement will be found for what ever contingency. For an example of that look at Norway. Nothing is perfect, but something closer to ideal may be found in future which ever way the vote goes.
ATB from George