In the EU we've qualified for every tournament bar the 94 world cup and the 84 and 2008 Euros. Pre the EU, we only one the World Cup once and had never been in a final before that. We didn't qualify for the 1964 Euros!!!
As for the quality of the premiership being diminished by fewer world...
I tend to agree with the sentiments however no one is really suggesting that this would be the only reason someone should vote remain, it's one of many.
As to the right to vote, I have no doubt there are many that vote in general elections do so on the back of headlines from their favourite...