Multiplayer isn't bad, but if it better meshed with the main game it could have been better. I admit MP added into some SP games can be fun. For example I really enjoyed the MP in God of War: Ascension. I've just kind of dead ended in the DAI MP. I've played it up to hard difficulty and most of the time people stick to the Halemsharal map and it gets boring to be honest. I don't really see a reason to keep trying to get better gear since it won't lead anywhere of much significance.
As to your original question about 'was it forced by EA?', I don't know, but my feeling is, no. I believe Bioware always wanted to put MP in DA:I and DA:O, in particular. Perhaps DA2 as well, although the design/setting of the game doesn't lend itself as well to MP.
With respect to your opinion about 'integrating' the two making MP more interesting...ah, hell no. If it requires integration into a SP campaign in order to be enjoyable, it is a failure. Moreover, we were promised until the devs twitter thumbs were bloody that the two modes would be totally separate and it was on launch. Changing that now....let's say that wouldn't be the best look and move on.
As a general rule, I have no problem with SP affecting MP, but the other way around is a big fat red flag. It practically screams 'pay to win'. But if people wanted - and got - to play their Inquisitor in MP matches, that wouldn't bother me in the slightest (as long as nothing they achieved in MP in any way opened up something in SP that couldn't also be unlocked via SP only).