I don't really care about the novels existence, but I don't even like that ME 3 relied on DLC from ME 2 for the story to make sense, which was not as severe as the extent to which DA:I relied on DLC for DA 2.
Agree about Arrival being incredibly plot relevant to ME3 yet barely explained at all in ME3, but DAI certainly didn't rely on DLC from DA2. Cory was introduced in DA2 DLC sure, but everything that is plot relevent to DAI can be learned in DAI. You can talk to Hawke and learn everything that he knows within DAI itself. DAI didn't do a whole lot right, but explaining the DA2 DLC in-game in DAI was one it did well. There is literally no need to play Legacy, because everything you would learn in it is told to you in DAI.
Everything the player needs to know about Cole is in DAI. He has backstory from one of the two books, but that merely expands his character, it isn't necessary to understand his character. So Masked Empire isn't even necessary at all to understand DAI, codexes and conversations with Cole, Briala, & Celene tell you everything you really need to learn from the books anyway.
The only time the tie-in novels really detract from the plot in-game is ME3, because the books are the only way you ever really learn why Cerberus and The Illusive Man got bat crap crazy. ME DLC (forgot the name, but the one where we go swimming with Leviathans) is also one instance where not playing DLC actively detracts from the story (you could argue the last DAI DLC is necessary for the story, but really it isn't necessary for the story of DAI, but it will be necessary [probably] for the story of DA4).
All-in-all the tie in novels can be ignored safely at the players choice. Stolen Throne was an excellent read and really tells you more about Loghain and makes him a far more sympathetic character, however it isn't neccessary. The other DA tie-ins are more or less the same, they add to the world but do not provide exclusive information that is necessary to know in-game. The original ME DLC (with Anderson and Saren) is completely 100% ignorable safely. It expands Anderson as a character, but doesn't really say anything directly necessary to play ME1 (or 2) effectively. The later stories do (sadly) start relaying information that is rather 'plot critical' and is never relayed in game.
I don't think tie-in novels are necessary, and I don't think ME:A would benefit from it. The only possible story an ME:A tie-in could have is pre-jump building the ARK and leaving the Milky Way. That is all information that *needs* to be relayed in game in ME:A anyway. If that info is not in ME:A (about a 5% chance from my estimations of BW's writing consistency) then the story will be completely unhinged from the rest of ME and would probably destroy the game. I wouldn't mind a novel expanding this information and providing characterization to some NPCs important to the pre-jump plot, but less relevant later (think Anderson in ME1), but all plot-relevant information in such a novel should be available in game anyway (Just like Mass Effect: Revelation).