OP question: "Why didn't industries from poorer European countries put the ones in the wealthier countries out of business after the EEC removal of internal tariffs?"
Well, let's just put it this way. If you were the finance minister or economic minister of your own poor European country, are you really seriously going to tell all the businesses in your country to do that to businesses in France, Britain or Germany, let's just say?
That kind of strategy would be like having your own country shoot itself in the foot. Because it's going to damage the economies of those three countries, who would logically have been among the leading buyers of products and/or services from your country.
The EEC, later the EC, eventually the EU, just like any other regional economic grouping, was designed to progressively build up and strengthen the economy of every member state, not just a select few at the expense of the rest.
And it's not meant to be like the soccer football WC either, where only one country can be champion, runner up, second runner up etc. respectively.
Granted, there will be some competition element, but the competition is mainly friendly and intended to improve efficiency, not to destroy anybody. A lot of it is more about mutually benefiting cooperation and collaboration, rather than sheer cut-throat dog-eat-dog competition.
Prosper thy neighbour, prosper thyself, then everybody will grow wealthier. Now, that is really the order of the day.
Tariffs have a trade restricting effect. So, removal of tariffs should rightly and logically create a trade boosting effect. For everybody in the grouping.
Well, at least that is the way I understand it, anyway.