While we don't know that "BioWare has learned their lesson" we do know that BioWare and EA are well aware of how successful the ME 3 MP was; and I am more inclined to believe that having both the developer and the publisher aware of the achievements of MP would (most likely) mean that they know of the fan backlash of the forced integration pre-EC. I am more inclined to believe that BioWare has a hand on the situation regarding MP, but since they have been relatively dodgy on the whole MP subject we can't really be sure either way.
Apart from the War Asset issue that ME 3 had at launch, MP had no negative impacts on the SP; at least not enough to warrant the uproar that the ending(s) received. Sometimes though, it almost feels that people believe that the horribleness of the conclusion to the ME trilogy is entirely because of the MP's addition to the game, and that by adding it to DA:I will somehow, magically make it's endings just as bad. The truth of the matter is that MP was caught in the middle of a bad situation and bad writing (IMO), and the general reaction was that the new and different elements to the game were the cause of ME 3's ills.
If a game's narrative is so flimsy that a MP mode would shatter all the lore, and sour the entire franchise then the writing must not have been very strong in the first place, and MP should be the least of players' worries.
I don't disagree with your logic, but here's an analogy I made a year or so ago:
Imagine Bioware as your kid, enrolled in school. She's always been a straight A student, 4 0 GPA, where you never had to really worry about her completing her assignments and doing well. Suddenly, out of nowhere, she gets a C on her report card (DA2, in this example). A C is average, nothing terrible... but you usually always expect straight A's, so it is highly unexpected.
But Bioware says they have learned their lesson, that the C was a fluke. And that she wants to go out for sports for the next semester - something she's never done before (MP is ME3). You have some misgivings, but since she is usually a A student, you take her word that she will be able to handle the responsibility and return to the high level of success... after all, lots of kids to out for sports (and have MP components), so we just need to chill out.
Except the next report comes out with very low marks and some very bad remarks from the school. And while the sports team had a better season than anyone expected, you are now seeing a trend where bad report cards indicate something is wrong and not just a fluke.
Would you let this kid keep playing sports? Or would you say "focus on getting your grades back up where they were before we even CONSIDER getting you back to sports" and only consider it when they returned to the higher standards you expected?
Lots of liberties taken with this metaphor, but to me it seems valid. One of the big problems with DA2 was the desire to change so much about the game design that A) players were thrown for a loop by the change and

the resulting extra work made the development path that much more difficult.
Adding a MP component is a huge undertaking, especially if you have little experience with it AND you aren't just copy-pasting the feature from another template. And even if you ignore budget and time schedules, you still have focus - focus from the lead designers, the producers, the entire executive team - focus that is now divided across different teams and development cycles. If you trust your other teams explicitly to make high quality content (or the bar isn't set that ugh to begin with, like the SP story component of most FPS), the. you have nothing to worry about. But if you need high quality and the team hasn't had the most sterling results in the most recent outings... is a shift in focus and attention the best idea?